economic analyses of world’s carbon markets · world’s markets are expected to be limited, and...
TRANSCRIPT
ECONOMIC ANALYSES OF WORLD’S CARBON MARKETS
By
Tajinder Pal Singh Bhatia
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy
Faculty of Forestry and Centre for Environment University of Toronto
© Copyright by Tajinder Pal Singh Bhatia 2012
ii
ECONOMIC ANALYSES OF WORLD’S CARBON MARKETS
Tajinder Pal Singh Bhatia
Doctor of Philosophy
Faculty of Forestry and Centre for Environment University of Toronto
2012
Abstract
Forestry activities play a crucial role in climate change mitigation. To make carbon credits
generated from such activities a tradable commodity, it is important to analyze the price
dynamics of carbon markets. This dissertation contains three essays that examine various issues
confronting world’s carbon markets.
The first essay investigates cointegration of carbon markets using Johansen maximum likelihood
procedure. All carbon markets of the world are not integrated. North American carbon markets
show integration and so do the CDM markets. For future, the possibilities of arbitrage across
world’s markets are expected to be limited, and carbon trading in these markets will be globally
inefficient. There is a strong need of a global agreement that allows carbon trade to prevent
climate change at the least cost options.
The second essay evaluates various econometric models for predicting price volatility in the
carbon markets. Voluntary carbon market of Chicago is relatively more volatile; and like other
financial markets, its volatility is forecasted best by a complex non-linear GARCH model. The
compliance market of Europe, on the other hand, is less volatile and its volatility is forecasted
best by simple econometric models like Historical Averages and GARCH and hence is different
iii
from other markets. Findings could be useful for investment decision making, and for making
choice between various policy instruments.
The last essay focuses on agent based models that incorporate interactions of heterogeneous
entities. Artificial carbon markets obtained from such models have statistical properties - lack of
autocorrelations, volatility clustering, heavy tails, conditional heavy tails, and non-Gaussianity;
which are similar to the actual carbon markets. These models possess considerably higher
forecasting capabilities than the traditional econometric models. Forecast accuracy is further
improved considerably through experimentation, when agent characteristics like wealth
distribution, proportion of allowances and number of agents are set close to the real market
situations.
iv
Acknowledgments
The completion of this research would not have been possible without the guidance, suggestions,
inspiration, support and love of many individuals.
First, I am greatly indebted to and would like to express my heartfelt appreciation to my
supervisor, Prof Shashi Kant for his valuable guidance, incessant encouragement and consistent
support throughout the course of this research. I thank him for involving me in this endeavor and
having confidence in my abilities to handle such a new and intricate research topic. The
discussions with him really broadened my knowledge and understanding of topic and equipped
me with necessary skills to carry out this task. This in fact had greatly improved the quality of
essays in dissertation. Without his critical reviews and intellectual inputs, this dissertation would
not have been possible in its present form. I am also indebted to the other members of my
research committee, namely Dr. Jagdish Nautiyal, Dr. David Nanang, Prof Martin Burda and Dr
Wang Sen for their valuable contribution and sparing time out of their busy schedule.
I am grateful for the academic and administrative support from the faculty members at the
Faculty of Forestry, the Centre for Environment and the Department of Economics. I would also
like to extend my gratitude to all the friends that I have made during the course of my research.
Financial support from the Nozzolillo Fellowship, Dixon Fellowship and Buckley Graduate
Scholarships at the University of Toronto is highly acknowledged. My sincere thanks are also
due to my employer, Forest Department, Government of Haryana, India for their supportive role
in sparing my services and sanctioning me study-leave to carry out this task.
I am highly grateful to my parents, Shri Ajit Singh Bhatia and Late Mrs. Manjit Kaur, for
inculcating the values of hard work and perseverance in me. Their deepest love and care have
shaped me to become an optimistic person and have helped me to remain positive and cheerful
even in times of overwhelming stress. My deep gratitude goes to my wife, Alakjot, for her
sacrifices, unconditional love and for all the support that she has given me during the past few
years. She endured all the pains so that I could accomplish my goal. It is truly a gift to have a son
like Anmol, who grows more precious with the years and has always been an overwhelming
source of joy- and for that I am very thankful. Last but not the least, I wish to thank God for
giving me such a wonderful environment that made my research possible.
v
Table of Contents
Acknowledgments .......................................................................................................................... iv
Table of Contents ............................................................................................................................ v
List of Tables................................................................................................................................... x
List of Figures ...............................................................................................................................xii
List of Appendices ....................................................................................................................... xiv
1 Introduction ................................................................................................................................ 1
1.1 Climate Change and Carbon Emissions .............................................................................. 1
1.2 Role of forests in carbon emissions and sequestration........................................................ 1
1.3 Role of carbon markets in forest investment decisions....................................................... 2
1.4 Literature Review................................................................................................................ 3
1.5 Organization of thesis.......................................................................................................... 7
2 Overview of World’s Carbon Markets ....................................................................................... 9
2.1 Carbon Trading ................................................................................................................... 9
2.2 Economic theory behind carbon markets ............................................................................ 9
2.3 Types of carbon markets ................................................................................................... 10
2.3.1 Compliance Markets ............................................................................................. 10
2.3.2 Voluntary markets ................................................................................................. 10
2.4 Existing carbon markets .................................................................................................... 11
2.4.1 EU Emissions Trading Scheme............................................................................. 11
2.4.2 Clean Development Mechanism (CDM)............................................................... 11
2.4.3 Carbon Markets in the USA.................................................................................. 12
2.4.4 Canadian Carbon Market ...................................................................................... 13
3 A cointegration analysis of Carbon Prices in EU and North America ..................................... 15
vi
3.1 Introduction ....................................................................................................................... 15
3.2 Theoretical concepts.......................................................................................................... 20
3.2.1 Cointegration......................................................................................................... 20
3.2.2 Testing for Stationarity and Structural Breaks in time-series ............................... 22
3.2.3 Lag length in the VEC Model ............................................................................... 23
3.2.4 Testing for Parameter Stability ............................................................................. 23
3.3 Data Description................................................................................................................ 24
3.3.1 European Climate Exchange (ECX) ..................................................................... 24
3.3.2 Chicago Climate Exchange (CCX) ....................................................................... 24
3.3.3 Regional Greenhouse Gas Initiative (RGGI) ........................................................ 25
3.3.4 California Climate Action Registry (CCAR) ........................................................ 25
3.3.5 Montréal Climate Exchange (MCeX) ................................................................... 25
3.4 Results and Discussion...................................................................................................... 27
3.4.1 Results for Unit Root Tests ................................................................................... 27
3.4.2 Carbon Market Integration at international level .................................................. 29
3.4.3 Long-run relationships of prices ........................................................................... 35
3.5 Summary and Conclusions................................................................................................ 37
4 Forecasting volatility of carbon markets .................................................................................. 41
4.1 Introduction ....................................................................................................................... 41
4.2 Volatility in carbon markets.............................................................................................. 45
4.3 Econometric Models used to test Volatility ...................................................................... 46
4.3.1 Random Walk........................................................................................................ 46
4.3.2 Historical average.................................................................................................. 46
4.3.3 Moving averages ................................................................................................... 46
4.3.4 OLS regression...................................................................................................... 46
4.3.5 Autoregressive conditional heteroskedasticity (ARCH) ....................................... 47
vii
4.3.6 Generalized autoregressive conditional heteroskedasticity (GARCH)................. 47
4.3.7 Asymmetric GARCH ............................................................................................ 48
4.3.8 Non-linear GARCH............................................................................................... 48
4.4 Testing for Stationarity and Structural Breaks .................................................................. 49
4.5 Evaluation Measures ......................................................................................................... 50
4.5.1 Root mean square error (RMSE)........................................................................... 50
4.5.2 Theil-U statistic ..................................................................................................... 50
4.5.3 LINEX loss function ............................................................................................. 50
4.6 Data ................................................................................................................................... 51
4.7 Results ............................................................................................................................... 51
4.7.1 Graphical analysis ................................................................................................. 52
4.7.2 Stationarity analysis .............................................................................................. 53
4.7.3 Volatility analysis.................................................................................................. 55
4.8 Summary and conclusions................................................................................................. 60
5 An Agent-Based Model of Carbon Markets............................................................................. 64
5.1 Introduction ....................................................................................................................... 64
5.2 Theoretical Framework ..................................................................................................... 67
5.2.1 Model of agents ..................................................................................................... 68
5.2.2 Model of price determination................................................................................ 69
5.2.3 Trading rules and expectation formations ............................................................. 71
5.2.4 Learning ................................................................................................................ 72
5.3 Adaptive Modeler- The Software Platform....................................................................... 73
5.4 Model Parameters.............................................................................................................. 74
5.4.1 Population Size...................................................................................................... 74
5.4.2 Wealth distribution................................................................................................ 74
5.4.3 Position distribution .............................................................................................. 75
viii
5.4.4 Basis of forecast .................................................................................................... 75
5.4.5 Trading rules ......................................................................................................... 75
5.4.6 Breeding ................................................................................................................ 76
5.5 Statistical Properties of Carbon Markets........................................................................... 76
5.5.1 Lack of autocorrelations........................................................................................ 78
5.5.2 Volatility clustering............................................................................................... 79
5.5.3 Heavy tails............................................................................................................. 79
5.5.4 Conditional heavy tails.......................................................................................... 80
5.5.5 Non-Gaussianity.................................................................................................... 81
5.6 The Simulation .................................................................................................................. 81
5.6.1 Lack of autocorrelations........................................................................................ 82
5.6.2 Volatility clustering............................................................................................... 83
5.6.3 Heavy tails............................................................................................................. 84
5.6.4 Conditional heavy tails.......................................................................................... 85
5.6.5 Non-Gaussianity.................................................................................................... 85
5.7 Experimentation with artificial carbon markets ................................................................ 85
5.7.1 Wealth distribution of agents (W)......................................................................... 86
5.7.2 Proportion of carbon allowances vis-à-vis total wealth (P) .................................. 87
5.7.3 Number of agents (N)............................................................................................ 88
5.8 Results and discussion of Experiments ............................................................................. 88
5.8.1 Changing W........................................................................................................... 89
5.8.2 Changing P ............................................................................................................ 90
5.8.3 Changing N ........................................................................................................... 91
5.8.4 Comparison with analytical models ...................................................................... 92
5.9 Summary and conclusions................................................................................................. 94
6 Conclusions, Policy Implications, Limitations and Future Work ............................................ 96
ix
6.1 Conclusions ....................................................................................................................... 96
6.2 Policy Implications............................................................................................................ 99
6.3 Limitations and Future Work .......................................................................................... 100
References ................................................................................................................................... 103
Appendix-1.................................................................................................................................. 113
x
List of Tables
Table Page
3.1 Data description for the price series of carbon markets in EU, USA and Canada for both Allowance and CER based assets (credits)…………….. 26
3.2 Results of ADF and Phillips-Perron unit root tests for carbon prices in the markets of EU, USA and Canada…………………………………… 28
3.3 Results of DF-GLS and Zivot-Andrews unit-root tests for carbon prices in the markets of EU, USA and Canada………………………………… 29
3.4 Results of Johansen’s multivariate co-integration tests for the carbon markets of EU, USA and Canada for both Allowance and CER based credits of EUA, CCXA, RGGIA, MONTLA, EUCER, and CCXCER (using 3 lags)….. 30
3.5 Results of Johansen’s multivariate co-integration tests for carbon markets of EU, USA and Canada for both Allowance and CER based credits of EUA, CCXA, RGGIA, MONTLA, EUCER, and CCXCER, taking five assets at a time (using 3 lags)…………………………………………………… 31
3.6 Results of Johansen’s multivariate co-integration tests for carbon markets of EU, USA and Canada for both Allowance and CER based credits of EUA, CCXA, RGGIA, MONTLA, EUCER, and CCXCER, taking four assets at a time (using 3 lags)…………………………………………… 31
3.7 Results of Johansen’s multivariate co-integration tests for only Allowance-based credits of CCXA, RGGIA and MONTLA in North America only (using 3 lags)……………………………………………… 33
3.8 Results of Johansen’s multivariate co-integration tests for carbon markets of EU and North America for CER-based credits EUCER and CCXCER (using 3 lags)…………………………………………………… 34
4.1 Summary statistics of the volatility series and tests for non-stationarity for ECX and CCX………………………………………………………... 54
4.2 Results of DF-GLS and Zivot-Andrews unit-root tests for carbon prices in ECX and CCX………………………………………………………… 55
4.3 Results for performance of econometric models for ECX Options Market……………………………………………………………………. 56
4.4 Results for performance of econometric models for ECX Futures Market 57
4.5 Results for performance of econometric models for CCX, Spot Market... 58
xi
5.1 Statistics for log returns for price in ECX and CCX…………………….. 80
5.2 Summary statistics for log returns of prices of actual and simulated markets…………………………………………………………………… 81
5.3 Statistics for the log returns for the price series of the simulated carbon markets of ECX and CCX……………………………………………….. 84
5.4 Results of experiments on artificial carbon markets for different wealth distribution of agents…………………………………………………….. 89
5.5 Results of experiments for changing the proportion of carbon assets…… 90
5.6 Results of experiments for changing N in ECX…………………………. 91
5.7 Results of experiments for changing N in CCX…………………………. 92
5.8 Results of forecasting ECX and CCX with GARCH (1, 1) and ABM...… 93
5.9 Results of forecasting CCX spot market with NL-GARCH and ABM…. 94
xii
List of Figures
Figure Page
3.1 Allowance and CER asset prices in carbon markets of EU and North America………………………………………………... 27
3.2 Graph of structural stability tests using Eigenvalue stability condition in VEC model for Allowance-based assets CCXA, RGGIA and MONTLA in North America…………………….. 33
3.3 Graph of structural stability tests using Eigenvalue stability condition in VEC model for CER-based assets EUCER, and CCXCER in EU and North America…………………………… 35
4.1 Price in ECX Options Market, Oct. 2006 to Jul. 2009……….. 52
4.2 Volatility in ECX Options Market, Oct. 2006 to Jul. 2009…... 52
4.3 Price in ECX Futures Market, Mar. 2006 to Jul. 2009……….. 52
4.4 Volatility in ECX Futures Market, Mar. 2006 to Jul. 2009…... 52
4.5 Price in CCX, Dec. 2003 to Jul. 2009………………………… 53
4.6 Volatility in CCX, Dec. 2003 to Jul. 2009…………………… 53
5.1 Cycle of an agent based model in Adaptive Modeler………… 73
5.2 Closing Prices ECX…………………………………………... 77
5.3 Log Returns ECX…………………………………………….. 77
5.4 Closing Prices CCX…………………………………………... 78
5.5 Log Returns CCX…………………………………………….. 78
5.6 Autocorrelations log returns ECX……………………………. 79
5.7 Autocorrelations log returns CCX……………………………. 79
5.8 Autocorrelations absolute log returns ECX…………………... 80
5.9 Autocorrelations absolute log returns CCX…………………... 80
xiii
5.10 Autocorrelations log returns ECX, VMP……………………... 82
5.11 Autocorrelations absolute log returns ECX, VMP…………… 82
5.12 Autocorrelations log returns CCX, VMP…………………….. 83
5.13 Autocorrelations absolute log returns CCX, VMP…………… 83
5.14 Autocorrelations log returns ECX, BAP……………………... 83
5.15 Autocorrelations absolute log returns ECX, BAP……………. 83
5.16 Autocorrelations log returns CCX, BAP……………………... 84
5.17 Autocorrelations absolute log returns CCX, BAP……………. 84
xiv
List of Appendices
Appendix Page
Appendix-1 Genetic Programming Flowchart, adopted from Koza (1992)………... 113
1
1 Introduction
1.1 Climate Change and Carbon Emissions
Climate change is recognized as one of the biggest challenges before mankind in the 21st
century. This thesis is devoted to carbon markets-a market-based solution designed to
address this problem. However, to understand the context within which these markets
operate, it is necessary to have some knowledge of the physical basis, causes and likely
impacts of climate change.
The problem of climate change is a consequence of the greenhouse effect- a natural
phenomenon that maintains an average temperature of 150C on earth, allowing life to
exist (IPCC 2007, 3). Greenhouse effect is caused by the natural presence of greenhouse
gases (GHGs), which trap part of the sun’s heat in the atmosphere. These gases are
carbon dioxide (CO2), methane, nitrous oxide, sulphur hexafluoride, hydrofluorocarbons
and perfluorocarbons. Due to excessive accumulation of these gases in the atmosphere,
the problem of climate change occurs. CO2 is the primary cause of the human induced
greenhouse effect, which comes mainly from burning fossil fuels and deforestation.
Another greenhouse gas, namely methane comes from burning of forests, ruminant
livestock, rice paddies, farms and landfill gas. Other GHGs, such as nitrous oxide (NOX)
comes from fertilizers and some chemical processes, halocarbons from refrigerant gases
and tropospheric ozone is released by combustion of hydrocarbons (Brohe et.al. 2009, pp.
6).
1.2 Role of forests in carbon emissions and sequestration
Climate change and forests are intrinsically linked and have both cause and effect
relationship with each other. Changes in global climate affect forests in a negative way
through higher mean annual temperatures, altered precipitation patterns and extreme
weather events. The most dramatic release of heat in the atmosphere occurs in forestry
sector on account of forest fires. In some rich regions of the world like southeast
Australia, western Canada, the western United States, and in southern Europe, this
appears to be a particularly growing problem. A second factor is the impact of warmer
2
weather on the spread of pests, such as mountain pine beetle, which kill trees and thereby
provide significantly more readily combustible material. In addition, windstorms in
Northern Europe also lead to very significant losses in forestry (Labbat and White 2007,
9-10). Furthermore, when forests are destroyed or over-harvested and burned, they can
become sources of carbon and contribute to climate change.
On the positive end, forests and wood products in long-term use trap and store carbon
dioxide, playing a major role in mitigating climate change. Trees help remove CO2 from
the atmosphere and converting it during photosynthesis to carbon, which they store in the
form of wood and vegetation, a process known as carbon sequestration (Brohe et.al.
2009, 10). In addition to trees themselves, the overall biomass of forests also acts as a
carbon sink. Therefore, serious action should be taken now to manage the complex
relationships between forests and climate change in a more holistic manner.
1.3 Role of carbon markets in forest investment decisions
In the present climate change scenario, carbon markets play a major role in forest
investment decisions. Looking at the global picture, various funds have been created by
different international organizations. The World Bank, for example, has created Forest
Carbon Partnership and Forest Investment Program, under which the Reduced Emissions
through Deforestation and Degradation (REDD) and the Clean Development Mechanism
(CDM) projects are funded in the developing countries. In return, emission credits are
awarded to the developed countries, which contribute to establishment of these funds
(REDD 2011, 1-2). Voluntary carbon markets like Chicago Climate Exchange also allow
buying and selling of forest carbon credits (CCX 2010, 2).
However, an investor like a forest manager or farmer at the local level will make forest
carbon investment decision purely on the basis of price dynamics of credits in the carbon
market. Her investment for carbon forestry will depend on the opportunity cost that she
has to incur by not subjecting her valuable land to other competing land uses like
agriculture, timber-forestry and recreation. Hence she will be very much interested in
understanding the price mechanism of carbon markets.
3
1.4 Literature Review
Functioning of carbon markets under the Kyoto Protocol is similar to that of any other
financial market. However, the commodity traded in carbon markets is CO2, which
affects the climate, a global public good (Brohe et.al. 2009, 22-24). Existing carbon
market research could be divided into three major categories: policy papers, theoretical
papers, and papers related to economic analysis. These are described in the following
paragraphs.
For policy matters, Johnson and Heinen (2004) made a future estimate of carbon trading
and projected that by 2010, the EU scheme would trade as much as $1 billion worth of
allowances each year. Their paper concluded that industry should get involved in carbon
trading and advance their interests. A policy paper by Godal and Klassan (2006)
examines the potential effects on permit prices and abatement costs of four compliance
rules governing emissions trade across sources and periods in the Kyoto Protocol: The
banking rule that allows excess permits to be used later; the restoration rate rule that
penalizes borrowing; the commitment period reserve rule that limits sales; and finally, the
suspension rule that restricts borrowing and sales. Veld (2005) considers socially optimal
carbon sequestration and abatement decisions under different expectations about future
carbon prices. It is shown that if carbon prices increase over time, consistent with
projections from integrated assessment models under various assumptions about future
climate-policy goals, it becomes optimal to delay certain carbon sequestration projects,
whereas the optimal timing of abatement projects remains unchanged.
As far as the theoretical papers are concerned, Copeland and Taylor (2005) provide a
trade theory view of the Kyoto Protocol. They demonstrate how several important results
in environmental economics, true under mild conditions in closed economies, are false or
need serious amendment in a world with international trade in goods. Convery and
Redmond (2007) have given a framework for market and price developments in the
European Union Emissions Trading Scheme (EU ETS). A comparison between carbon
taxes and emissions trading has been made by Mandell (2008). He argues that in practice,
different emitters of a particular pollutant are sometimes subjected to different control
mechanisms. This paper is aimed at analyzing whether, from an efficiency point of view,
4
it is preferable to divide a regulated economy into two sectors, subjecting one sector to
cap-and-trade and the other to an emissions tax, rather than adopting the cost effective
approach of subjecting the entire economy to either cap-and-trade or an emissions tax. It
shows that mixed regulation can be superior. Streck, Tuerk and Schlamadinger (2009)
examine offset projects and argue that forestry offsets should be integrated with EU ETS
for increasing efficiency. Mehling and Haites (2009) and Persson (2009) describe
mechanism for linking carbon markets theoretically. Anger (2007), by way of simulation
studies, assesses the economic impacts of the linked carbon markets; whereas, Haites and
Wang (2009) prescribe a framework for ensuring the environmental effectiveness of such
linked markets.
Among papers relating to economic analysis, Uhrig-Homburg and Wagner (2007)
examine the future price dynamics of CO2 emission certificates through an empirical
analysis of relationship between spot and future markets in EU ETS. Oberndorfer (2008)
carries out an econometric analysis on EU emission trading scheme. This paper claims to
be the first econometric analysis on stock market effects of the EU Emission Trading
Scheme. The focus of research is specifically on the electricity units. It analyses
electricity stock return reactions to changes in EU Emission allowance prices. A big
limitation of this paper is that it is focused only on the electricity firms. Paolella and
Taschini (2008) carries out an econometric analysis of emission allowance prices in
North American SO2 and CO2 markets through examination of their stylized facts.
Seifert, Uhrig-Homburg and Wagner (2008) study the dynamic behavior of CO2 spot
prices. Benz and Trück (2009) analyze the short-term price behavior of carbon
allowances in EU ETS through review of stylized facts and modeling the return of
emission allowances.
Despite of the volume of research in carbon markets, there are some gaps in the literature,
which need to be addressed by way of further exploration of this area. Such gaps are
described subsequently.
First, market integration and the value of diversification of portfolios among countries is
an important factor in investment decision making. The same is true of carbon markets.
5
Due to the recognition of trade in emission allowances or permits in organized carbon
markets for meeting emission reduction targets under Kyoto Protocol, several national
and regional carbon markets have been established around the world. Hence there is a big
need to unify carbon market instruments to overcome problems across fragmented and
less efficient markets (Zoellick 2007). A deep and global market can deliver significant
benefits to all participants, including low-cost abatement options and helping set effective
price signals. It will also bring opportunities for deepening sustainable development that
can be supported through enhanced technical and financial cooperation. Increasing
integration of world carbon markets could imply better diversification opportunities and
fewer tendencies for arbitrage (World Bank 2007, 7-8). Also Majid et.al. (2008) suggest
that investors should invest internationally because of the risk reduction that stems from
the lower correlation between assets of different countries. So from research point of
view, study of market integration is the first and foremost factor for the emerging carbon
markets. A lot of research has been carried out for financial markets in this direction, for
example by, Su et.al (2007), Moroza (2008), and Elfakhani et.al (2008). In the case of
forest products, market integration of the US and Canadian softwood lumber markets is
analyzed by Shahi, Kant and Yang (2008) using Vector error correction model and the
Johnson approach. However, such integration techniques have hardly ever been used to
explore the possibility of unification of world carbon markets.
Second, carbon markets, despite their voluminous growth, have experienced a lot of
fluctuations since their very inception, which are caused by market uncertainties. A full
understanding of volatility of carbon prices is, therefore, critical from multiple
perspectives as it poses a significant threat to industries and economies in a carbon
constrained world. First, the short-run price volatility could discourage the deployment of
new capital intensive abatement technologies, by giving rise to an option value from
delaying irreversible investments (Chao and Wilson, 1993). Second, for most of the
investment decisions, volatility shall determine the return on capital. Third, price
volatility may have some major disruptive effects on the price dynamics of the market.
Lastly, forecasts of carbon price volatility could be important inputs into macro-
econometric models and market risk assessment calculations like value at risk and; for
the purpose of forecasting return series, more accurate intervals can be obtained by
6
modelling volatility of returns (Yu, 2002). Price volatility, therefore, is one of the key
determining factors in the choice of a carbon policy instrument. A lot of research has
been carried out forecasting volatility in the financial markets other than carbon markets,
for example, by Yu (2002), Balaban (2006), Wang and Lin (2007) and Bernard et.al
(2008). For energy markets, a model for forecasting oil markets has been developed by
Kang, Kang and Yoon (2008). However, relatively little work has been done so far on
modeling and forecasting carbon market price volatility from an econometric or risk
management angle.
Lastly, the traditional approach for forecasting price in financial markets is through use of
analytical models (Tesfatsion 2005, 1). Complexity of carbon markets represents a big
challenge to that approach. Most analytical models make simplifying assumptions, such
as perfect rationality and homogenous agents, which may cause biased results and
demand alternative methods. Agents like different countries, organizations, industries and
individuals are involved in the process of carbon trading, both on the demand side and the
supply side. These agents interact with each other and with the overall trading-
environment to evolve the emergent behavior of these markets (Axelrod and Tesfatsion
2005, 2-3). Therefore for obtaining better forecasts, it is necessary to incorporate agent
behavior in carbon markets. Agent based models have been found to give promising
results for financial markets (LeBaron 2000). They have been used in the past to model
ecosystems (Grimm 1999), economic systems (Thebaud and Locatelli 2001), and social
systems (Axelrod 1997). Hoffmann et.al. (2007) make use of social simulation in linking
micro-level investor behavior and macro-level stock market dynamics. In financial
markets, agent-based computational modeling is used by Chen and Liao (2007), who
examine the possible explanations for the presence of the causal relation between stock
returns and trading volume. Chen and Yeh (2001) use two well known hypotheses in
economics to illustrate how emergent properties can be shown in an agent-based artificial
stock market. Situngkir and Suya (2005) construct an agent-based model as a form of
advanced study for financial economic post-statistical-data and micro-simulation
analysis. These studies explain how agent based modeling is used to describe the
behavior of various stock markets. However, these techniques have hardly ever been used
7
to model the newly emerging carbon markets and could be used to study their behavior
also.
1.5 Organization of thesis
To fill the identified gaps in the existing literature, this research carries out detailed
economic analyses of world’s carbon markets. The specific objectives of this thesis are:
(i) to analyze the long-run market integration indicated by cointegration between carbon
prices in various markets of the world; (ii) to forecast short-term volatility in different
carbon markets; and (iii) to develop an agent based model of carbon markets and
compare it with analytical models for the purpose of forecasting. The dissertation is
composed of three independent papers that are written in journal article style and address
these issues.
The first paper addresses the long-run integration of carbon markets at the interregional
level using the Johansen full information maximum likelihood procedure for testing co-
integration. The main findings of the paper suggest that all carbon markets of the world
are not integrated. North American carbon markets are integrated with each other and so
are the CDM markets. For future, it is expected that the possibilities of arbitrage across
the global markets will be limited, and the carbon trading in these markets will be
globally inefficient. Hence, there is a strong need of a global agreement that allows global
carbon trade to prevent climate change at the least cost options.
The second paper evaluates the performance of various econometric models, both simple
and complex, for predicting short-term price volatility in European Climate Exchange
(ECX) and Chicago Climate Exchange (CCX). Results suggest that the voluntary carbon
market of CCX is relatively more volatile and is forecasted best by complex model like
non-linear GARCH; and this behavior of this voluntary market is similar to that found in
other financial markets and energy markets. The compliance market of ECX, on the
other hand, is less volatile and is forecasted best by simple econometric models like
Historical Averages and GARCH (1, 1) and hence is different from other markets. These
results might be useful for anyone interested in carbon market volatility.
8
The third paper considers agent based models, which are the bottom-up simulations of
actions, incorporating interactions of such heterogeneous entities in the carbon market.
Artificial carbon markets obtained from such agent based models for the spot markets of
European Climate Exchange (ECX) and Chicago Climate Exchange (CCX) have stylized
facts – lack of autocorrelations, volatility clustering, heavy tails, conditional heavy tails,
and non-Gaussianity; which are similar to the actual carbon markets. These models are
found to possess considerably higher forecasting capabilities than the traditional
econometric models. Experiments performed on these artificially simulated carbon
markets by changing wealth distribution of agents, by varying the distribution of
proportion of carbon assets, and lastly by changing the number of agents in the carbon
market, show that forecast accuracy is further improved considerably, when the values of
these agent parameters are closer to real market situations. Agent based models could
play a key role in mimicking the real world carbon markets and could provide an
alternative to the analytical models for better forecasting.
The remaining dissertation is organized as follows: Chapter 2 gives an overview of
carbon markets. Chapter 3 contains the first essay titled “Cointegration of EU and North
American Carbon Markets”. Chapter 4 comprises the second essay titled “Forecasting
Volatility of Carbon Markets”. Chapter 5 consists of the third paper titled “An Agent
Based Model of Carbon Markets”. Lastly, Chapter 6 covers the summary and
conclusions. In addition, since this dissertation is written in an independent paper style
format, some repetitions in explanation of terminology and other aspects of carbon
markets are bound to occur here and there in different chapters.
9
2 Overview of World’s Carbon Markets
2.1 Carbon Trading
Carbon-trading is an administrative approach used to control emission of Carbon dioxide
(CO2) by provision of economic incentives. A central authority sets a limit or cap on the
amount of carbon that can be emitted (Marcu 2006, pp. 8). Companies, individuals or
other groups are issued emission permits and are required to hold an equivalent number
of allowances (or credits) which represent the right to emit a specific amount. The total
amount of allowances and credits cannot exceed the cap, limiting total emissions to that
level. Companies that need to increase their emission allowance must buy credits from
those who pollute less (Soleille 2006). In effect, the buyer pays a price for emitting, while
the seller is rewarded for having reduced emissions by more than was needed. Over the
last few years, such trading has given rise to the evolution of carbon markets.
2.2 Economic theory behind carbon markets
For stabilizing the levels of carbon in the atmosphere, we need not only to focus on forest
conservation, clean energy technologies and emission reduction strategies, but also must
generate the market pull for them. Carbon markets are among the most innovative and
cost-effective methods for creating market pull for forestry credits and new clean energy
technologies while, at the same time, putting a price on emission and thereby providing
incentives for people to emit less (Karmali 2010, pp. 61). Carbon markets are able to
achieve this aim because they help channel resources toward the most cost effective
means of reducing GHG emissions. They also punish those who emit more than an
established quota, and reward those who emit less (Stern 2006, pp. 27). The market based
approach also allows third-party players, such as speculators, to enter the fray and make
investments in green endeavour. Other interested parties also can get involved. If, for
example, an environmental group wants to see emissions decrease below a regulated
target, they can raise money to buy and retire emission allowances. This drives up the
costs of emissions and can force emitters to become more efficient (Bayon, Hawn and
Hamilton 2007, 55).
10
2.3 Types of carbon markets
The term carbon market refers to the buying and selling of emissions permits that have
either been distributed by a regulatory body or generated by Greenhouse Gas (GHG)
emission reduction projects. GHG emission reductions are traded in the form of carbon
credits, which are equal to one metric ton of CO2, (tCO2e), the most common greenhouse
gas (IPCC 2007, 1-4). Carbon markets can be separated into two major categories:
compliance markets and voluntary markets.
2.3.1 Compliance Markets
Compliance markets are created and regulated by mandatory regional, national, and
international carbon reduction regimes like the Kyoto Protocol (Brohe et.al. 2009, 12).
The biggest success of compliance markets so far has been to send market signals for the
price of mitigating carbon emissions. The total traded volume in the compliance carbon
market grew from 4.8 Giga-tons (Gt) in 2008, to 8.7 Gt in 2009 (Kossoy and Ambrosi
2010, 1-2). Demand is driven by the emitters who must operate within proportion of the
cap that has been allocated to them. An emitter has to buy additional emission permits, as
soon as it exceeds the amount that has been initially allocated to it. However, demand
falls due to employment of mitigation technologies or due to fall in the production output
of the firm (Brohe et. al 2009, 25-26).
2.3.2 Voluntary markets
Voluntary carbon markets function outside of the compliance markets, enabling
companies and individuals to purchase carbon offsets on a voluntary basis. The voluntary
market reflects the sum of all transactions of carbon credits and allowances, where the
final purpose of cancelling or retiring the carbon credit is not to comply with legislation
or to fulfill agreements between companies and governments. The voluntary carbon
market, although much smaller than the compliance market, is now growing rapidly
(Point Carbon 2004).
11
2.4 Existing carbon markets
Kyoto Protocol established the principle of trading carbon emissions between countries to
reduce GHGs by following low cost options. However, the actual emitters are not
countries themselves, but the companies, transport systems, logging industries and
households operating within the boundaries of those countries. Carbon trading is
therefore carried out by such agents due to fixing of emission reduction targets by the
regulators or as a matter of emissions reduction on voluntary basis. To facilitate this
mechanism of emissions trading, various carbon markets have come up across the length
and breadth of the globe. Some of these markets are compliance markets and others are
voluntary ones. Carbon markets that have been considered in this dissertation are
described briefly in this section.
2.4.1 EU Emissions Trading Scheme
EU ETS is the largest carbon market established in the world till date. Nearly 10,000
installations are included in its scope, which comprise of thermal power stations more
than 20 MW, mineral oil refineries, coke ovens, iron production and processing, mining,
glass, ceramics and paper and pulp. EU ETS was launched in 2005 and is a cap-and-trade
scheme that covers nearly half of EU’s carbon emissions (Soleille 2006). To ensure
market liquidity, a trading platform, namely European Climate Exchange (ECX) has been
established. Its primary function is to contribute to the liquidity in the market and offer
customers the benefits of reduced transaction costs, lesser risks, guarantee of anonymity
and price transparency (Labbat and White 2008, 143-147). Data from ECX have been
used for the purpose of this dissertation.
2.4.2 Clean Development Mechanism (CDM)
Under the Clean Development Mechanism (CDM), a developed country (also called
Annex-I country under Kyoto Protocol) invests in a developing (Non-Annex-I) country
for the purpose of reducing GHG emissions and also promoting sustainability principles
in the latter. For every ton of CO2 reduced or absorbed through the project, the investor
receives a Certified Emission Reduction (CER). Development of a CDM project can be
unilateral, bilateral or multilateral. Unilateral project development is planned and
12
financed within a developing country, whereas, in a bilateral model, one or more
developed countries finance and implement the project (Brohe et.al 2009, 42-53).
Multilateral CDM projects take the approach of a mutual fund in which the investments
flow from a centrally managed fund like the one by World Bank to projects in the host
countries. Each of these different structures has advantages and disadvantages in terms of
incentives, risks and transaction costs. Most of the forestry projects in developing
countries fall in this category.
2.4.3 Carbon Markets in the USA
While the United States of America pioneered emissions trading in its regulation of
sulphur dioxide (Feldman and Raufer 1987), the development of carbon trading at
national level has been slow to emerge. However, some action has been taken at the
regional and State level. In addition to establishing three regional emissions trading
schemes, 17 states have established state-wide emission targets. The initiatives are likely
to result in a national emissions trading system with long term aim of reducing national
emissions by 80 percent by 2050 (White House 2009, 1-2). Different carbon markets that
are in operation or development within the US are described here.
2.4.3.1 Chicago Climate Exchange (CCX)
CCX was the first voluntary, legally binding rule-based greenhouse gas emission
reduction and trading system launched in 2003. Carbon credits traded in CCX are called
Carbon Financial Instruments (CFIs). The exchange restricts trading to members who
have voluntarily signed up to its mandatory reductions policy (Bayon, Hawn and
Hamilton 2007, 50). The majority of trade in CCX is allowance based, rather than project
based. Whenever the offset projects are used, CCX requires that an approved third party
organization verify that the project’s emission reductions are real and they meet standards
set by the exchange. Data from CCX has been extensively used in this dissertation.
2.4.3.2 Regional Greenhouse gas Initiative (RGGI)
RGGI was the first mandatory US cap-and-trade program for CO2. Ten northeastern and
mid-Atlantic states, namely Connecticut, Delaware, Maine, Maryland, Massachusetts,
13
New Hampshire, New Jersey, New York, Rhode Island and Vermont are part of this
initiative (Brohe et. al 2010, 153-155). These participating states negotiated state-wide
caps largely on the basis of historical emissions. Aggregated, these caps form the regional
RGGI cap. The cap is set on fossil-fuel fired power plants of at least 25 MW, covering
about 225 facilities (RGGI 2010, 1-2). It also allows for the use of offset projects for
compliance.
2.4.3.3 Western Climate Initiative (WCI)
WCI plans to lay the foundation for an international cap-and-trade program that would
involve both the US and Canada. It involves the states of Arizona, California, Montana,
New Mexico, Oregon, Utah and Washington, and the Canadian provinces of British
Columbia, Manitoba, Ontario and Quebec (Brohe et. al 2010, 168-169). Various other
states have joined as observer states also. The WCI program is expected to cover about
90 percent of GHG emissions in participating American states and Canadian provinces
once it is fully implemented in 2015 (WCI 2010, 1-2).
2.4.3.4 Midwestern Regional Greenhouse Gas Reduction Accord (MGA)
MGA was established in 2007 by six states of USA, namely Illinois, Iowa, Kansas,
Michigan, Minnesota and Wisconsin and one Canadian province of Manitoba. They set a
long term target of emission reduction below 60-80 percent below current emission levels
and develop a multi-sector cap-and-trade system to achieve this target (Hight and Silva-
Chavez 2008).
2.4.4 Canadian Carbon Market
For tackling the issue of climate change, causing severe environmental and economic
risks, the Government of Canada has decided to adopt intensity-based greenhouse gas
(GHG) emissions reduction targets. In addition to following technology based methods,
the market solution of carbon markets is also prescribed for. Therefore, the Montréal
Climate Exchange (MCeX) has been established in collaboration with the Chicago
Climate Exchange (CCX) to launch trading of futures contracts. These contracts allow
regulated industrial participants to manage their emissions risks at the lowest cost while
14
also creating continuous incentives for technological innovation. The new MCeX
contract, traded on the Montréal Exchange's electronic trading platform gives key
regulated industrial emitters and other potential stakeholders the price signals needed to
measure the price of CO2 (MCeX, 2010).
Various other carbon markets have also emerged in different part of globe like those in
China, Japan, Australia, India and New Zealand (Brohe et. al 2010, 198-244). However,
most of these markets are in nascent stage and very little data are available from them for
carrying out any meaningful econometric analysis. Therefore, this dissertation makes use
of data from the carbon markets in EU and North America only. With availability of new
data, the analysis of subsequent chapters can be extended to other parts of the world also.
15
3 A cointegration analysis of Carbon Prices in EU and North America
Abstract
Several national and regional carbon markets have already become functional around the
world, and there is a need to integrate them to overcome problems across fragmented and
less efficient markets. In this chapter, integration of the EU and North-American carbon
markets is studied using the Johansen full information maximum likelihood procedure for
testing cointegration. All carbon markets across the EU and North America are not
integrated. However, co-integration is observed among the certified emission reduction
assets traded in the EU and North America, depicting the integration of clean
development mechanism project markets. In addition, cointegrating relationships are
present within allowance-based markets of North-America, but allowance markets of the
EU do not show co-integration with the North American counterparts. For future, it is
expected that the possibilities of arbitrage across the global markets will be limited, and
the carbon trading in these markets will be globally inefficient. Hence, there is a strong
need of a global agreement that allows global carbon trade to prevent climate change at
the least cost options.
Key words: Carbon markets, Climate Change, Cointegration, and Johansen maximum
likelihood procedure.
3.1 Introduction
Climate change through greenhouse gas (GHG) emissions is now established as a major
policy challenge for governments and the international policy makers. To address this
issue, Kyoto Protocol was put in place in 1992 by the United Nations Framework
Convention on Climate Change (UNFCCC). One of the main mechanisms of GHG
reduction recommended by the Protocol is trading of emission allowances or permits,
primarily of carbon dioxide (CO2), in organized markets. Several national and regional
carbon markets have been established around the world, in which a variety of specialized
instruments are traded. Europe has emerged as a leader in the emissions trading industry
16
with the European Union Emissions Trading Scheme (EU ETS) being the world’s largest
single market for CO2 emission allowances, accounting for approximately 97% of the
global transactions in 2010 (Linacre, Kossoy and Ambrosi 2011, 1). China has remained
the largest Clean Development Mechanism (CDM) project seller during this time. The
most significant change in policy landscape over the past years, however, is the re-
emergence of the United States in the climate change debate. The Waxman-Markey Bill
of the U.S. provided for the international emissions allowance trading (Daskalakis,
Psychoyios and Markellos, 2009). Though there was not enough support to pass this
legislation at the federal level, many carbon markets have already become operational at
the regional levels. The demand of carbon credits from EU and USA is expected to create
an opportunity for developing countries also to become part of carbon market mechanism
(Capoor and Ambrosi, 2009). Regarding future of carbon markets, there are various
reasons for optimism. The Copenhagen accord of the UNFCCC prescribes to continue the
carbon market approach to enhance the cost-effectiveness of, and to promote mitigation
actions of climate change (CoP, 2009). The same has been reiterated by Cancun
conference also. Progress at Cancun has been welcomed by the market and helped to
restore some confidence in UN negotiations on climate change. Various national and
local initiatives, for example, California’s cap-and-trade scheme, Western Climate
Initiative and Regional Greenhouse Gas Initiative have noticeably picked up and may
offer the potential to collectively overcome the international regulatory gap. Apart from
these initiatives, various carbon markets have gained increasing traction in developing
economies such as Brazil, China, India, and Mexico (Kossoy and Ambrosi 2010, 4-5).
Carbon markets have been established in different countries and regions, depending on
the differences in their level of commitment to tackle climate change and the differential
amount of reductions required under Kyoto Protocol. As a result, price structure of
carbon might be different among them, resulting in inefficiencies (Linacre, Kossoy and
Ambrosi 2011, 7-22), because prices do not fully reflect the available information in the
market in this case. However, market integration ensures efficiency gains, increased
market liquidity, and the reduced volatility (Flaschsland, Marschinski and Edenhofer
2009) by making carbon credits available to right agents at the right price through
removal of information gaps. In political terms, integration between different emission
17
trading schemes, can ensure carbon-market-based cooperative climate policy across
international borders (EU Commission, 2009). This chapter investigates an important
issue in international carbon trading, which has got significant enviro-political
implications: Are carbon markets regionally segmented or have they evolved into a
global, integrated market, thus deriving the benefits of economic efficiency and
international cooperation? Given the importance of carbon trading under present climate
change scenario, this question is also of high relevance for framing of environmental and
economic policy by different countries.
This analysis is motivated by the following factors: First, carbon markets have emerged
at regional, national and international levels. The regional segmentation has been
established due to different policy stands taken by the respective governments at not only
the national levels but also at provincial levels in different countries. To drive emission
reductions, countries and regions adopt a range of domestic policies that may focus on
cap-and-trade schemes, baseline and credit mechanisms, renewable energy and energy
efficiency certificates, carbon taxes, subsidies or emission standards. In many cases,
multiple policy approaches are being used that may be complementary and sometimes
contradictory, and which often have different costs and benefits accruing at different
times and geographical scales (Kossoy and Ambrosi 2010, 25). As a result, carbon
markets established in different regions are governed by specific demand and supply
patterns. Second, climate policy at the global level is going through a period of critical
transformation. There is a need to unify carbon market instruments to overcome problems
across fragmented and less efficient markets. In words of Zoellick (2008), “A deep and
global market can deliver significant benefits to all participants, including by expanding
low-cost abatement options and helping set effective price signals. It will also bring
opportunities for deepening sustainable development that can be supported through
enhanced technical and financial cooperation”. Increasing integration of world carbon
markets could imply better diversification opportunities, less concerns about availability
of carbon credits, more competition among the supplying regions and less tendencies for
arbitrage (Stern 2006). Third, with the growing number of emission trading systems,
there has been an increased interest in the feasibility of integrating distinct programs, as
firms may take advantage of a range of marginal abatement costs of firms in the
18
integrated system (Flaschsland, Marschinski and Edenhofer 2009). At the countries’ level
also, when different trading schemes are linked, the prices tend to equalize. Sources in
the countries with higher permit price purchase permits from sources in the country
where price of permits is lower until the prices and hence marginal abatement costs
(MACs) are equalized across the two countries with total emissions remaining the same
(Kruger, Oates and Pizer, 2007). Studying integration of carbon markets can be helpful in
taking policy level decision of linking various emission trading schemes. The first step in
the study of integration of carbon markets is examination of the Law of One Price (LOP)
among different carbon markets of the world. The existence of the LOP between various
markets would indicate that the CO2 prices in different markets move together, and the
differences in local policies and price mechanisms should not be of great concern for
overall international carbon trading. Hence the existence of LOP between national and
regional carbon markets is examined in this chapter.
The importance of market integration using LOP is very well documented in the
economics literature and various authors, including Egert and Kocenda (2007), Florus
and Vougas (2008) and Valadkhani and Chancharat, (2008) have tested market
integration for primary equity markets. He et.al. (2010), and Maghyereh and Kandari,
(2007) have carried out market integration studies for oil, electricity and natural gas
markets. Uri and Boyd (1990), Jung and Doroodian (1994), and Shahi, Kant and Yang
(2006) have tested LOP for integration of softwood lumber markets. Regarding carbon
markets, Anger (2008) assesses the economic impacts of linking the EU emissions
trading schemes to emerging schemes beyond Europe in the presence of a post-Kyoto
agreement in 2020. His paper concludes that from an efficiency perspective, the most
desirable future climate policy regime should be represented by a joint trading system
facilitating international emissions trading between ETS companies across the countries.
He also favours linking cap-and-trade systems with the Clean Development Mechanism
projects in developing countries to ensure large scale cost savings. Mehling and Haites
(2009) discuss mechanisms for linking greenhouse gas emission trading schemes. The
mechanisms are legal and institutional arrangements to integrate between various
emissions trading schemes and sustaining their integrity over time. Persson (2009) argues
that linking North east states of the US mitigation program to the EU emission trading
19
scheme would encourage a change of the federal US policy, which traditionally has
followed action taken at the state level. Flaschsland, Marschinski and Edenhofer (2009)
have devised a framework to assess direct bilateral cap-and-trade linkages through an
analysis of the economic, political and regulatory framework that indicates potential
benefits along with a number of potentially negative side effects. Their study indicates
that, due to presence of market distortions or terms-of-trade effects, international
emissions trading may not be welfare-enhancing for all countries. Their paper also
assesses a linkage between the EU ETS and a prospective US trading system and
identifies the major trade-offs. Sterk and Kruger (2009) examine the current emissions
trading debates in the EU and the USA and analyze the prospects for creating a
transatlantic carbon market. They question the compatibility of the design of USA
emissions trading schemes and the EU ETS. Their paper argues that crucial differences
relate to the stringency of targets, the recognition of offsets, and price control
mechanisms and suggests that the two sides should seek a way forward that reconciles
potentially different climate policies. The paper recommends that the USA and the EU
should consider an effort to harmonize carbon prices and should have mechanisms that
allow periodic recalibration, which would allow each to adjust to new technology, react
to developing-country climate policies, and learn from each other. However, none of
these papers focus on actual price dynamics in carbon markets for exploring the
feasibility of integrating them. To the best of my knowledge, there is no study that has
tested the LOP for different national and regional carbon markets or emission trading
schemes.
This chapter addresses the integration of carbon markets at both international and inter-
regional levels. The main objective of this chapter is to test the LOP among the carbon
markets of EU and North America. Other carbon markets of the world are still in the
nascent stages (Benz and Trück 2009) and not enough data are available from them to
carry out any meaningful econometric analysis. In particular, the structure of the carbon
markets of EU and North America is analyzed using the Johansen full information
maximum likelihood procedure for testing co-integration. The presence of cointegration
between the prices of different geographic markets and different carbon assets is
interpreted as evidence of carbon market integration. The study contributes to the existing
20
literature in three major aspects. First, three carbon markets namely EU, US and Canada
have been covered, thus expanding the sphere of research from EU ETS, which had been
the prime focus of research in major studies by, for example, Bohringer, Hoffman and
Manrique-de-Lara-Perate (2006), Benz and Trück (2009) and Daskalais, Psychoyios and
Markallos (2009). Second, in this chapter, entire discussion is based on price dynamics of
carbon markets rather than being a mere reflection of the policy and regulatory
perspectives. Finally, not only the CO2 allowance prices, but the prices of certified
emission reductions (CERs) have also been included. This is specifically important, as
CERs are generated from the Clean Development Mechanism (CDM) projects, mainly in
the developing countries. The findings of this chapter suggest that all existing carbon
markets across the EU and North America are not integrated. However, cointegrating
relationships are present within allowance-based markets of North-America.
Cointegration is also observed among the certified emission reduction assets traded in EU
and US, depicting the integration of clean development mechanism project markets.
Allowance-based markets of EU do not show any integration with the North American
carbon markets, requiring policy initiatives on linking the two schemes.
This chapter is organized as follows. Section 3.2 explains the theoretical concepts of
cointegration and empirical estimation. The data set and their time series properties are
described in Section 3.3. Results of Johansen cointegration procedure are reported in
Section 3.4 before policy conclusions and issues of further research are presented in
Section 3.5.
3.2 Theoretical concepts
3.2.1 Cointegration
Cointegration of prices in different markets means that change in price in one market will
lead to change in price in other markets, which means cointegrated markets are not
independent (Shahi, Kant and Yang 2008). Mathematically, a (P X 1) vector of time
series, yt, is co-integrated if each of the elements of yt is I (1), that is, non-stationary with
a unit root, whereas some linear combination of the series a’yt is stationary, or I(0), for
some nonzero (P X 1) vector, a (Engle and Granger 1987). Johansen (1988, 1995) and
21
Johansen and Juselius (1990, 1992) have suggested maximum likelihood procedures for
testing of co-integration in a p-dimensional finite-order vector auto-regression (VAR)
model. The procedure gives estimates of system’s co-integrating vectors and their
weights. These estimates are used to test relevant economic hypothesis. Moreover, the
maximum likelihood estimates are symmetrically distributed, median unbiased and have
mixed normal distributions (Johansen 1992). The system of equations is
,1
1 tt
k
i
tit DyAy ε+Φ+=∑=
− ),0(~ Ωpt Nε , Tt ,.....,1= (3.1)
where yt is a vector of empirical variables, Dt is the vector of deterministic terms, which
can contain a constant, a linear trend, seasonal dummies, or other regressors that are
considered fixed or nonstochastic, k is the lag length, εt is a vector of error terms assumed
to be independent identically distributed, i.e., Np (0, Ω), and T is the number of
observations.
Johansen maximum likelihood estimation uses a rank test to define the number of
cointegrating vectors r that can be found in the data. The rank is determined by estimating
the p-dimensional VAR (k) model in Equation (3.1) that can be re-parameterized as a
vector error correction (VEC) model,
ttt
k
i
itt Dyyy ε+Φ+∆Γ+Π=∆ −
−
=
− ∑ 1
1
1
1 , ),0(~ Ωpt Nε , Tt ,.....,1= (3.2)
where ∆ is the first difference operator, ∆yt is a vector of I(0) processes,
,1
∑+=
−=Γk
ij
ji A
and )(1
∑=
−−=Πk
i
iAI (3.3)
is the matrix of long-run coefficients and can be decomposed as Π=α β’. The matrix α is
the matrix of weights and represents the short-run effect of disequilibria indicating the
22
speed of adjustment to the equilibrium. β is the matrix of long-run dynamics of the
variables yt. The columns of β are the co-integrating vectors representing the stationary
linear combination of variables yt. The rank r of the long-run matrix, Π, determines the
number of co-integrating vectors in the system. Johansen (1988, 1995) and Johansen and
Juselius (1990, 1992) have suggested two likelihood ratio-based tests that are called the
trace test and the maximum-Eigenvalue test for testing the rank of Π. Different values for
the number of co-integration vectors have different implications: (1) if the rank of Π is
zero, the variables are not co-integrated and the relationship should be tested using
ordinary least-squares (OLS) in difference (Banerjee et al. 1993, p. 256); (2) if the rank of
Π is full, the series yt are individually stationary and OLS in levels can be used for
testing; (3) if the rank of Π is more than zero and less than the number of variables, the
series yt are co-integrated and the rank indicates the number of linearly independent co-
integrating relations among the variables in yt (Dickey et al. 1991).
3.2.2 Testing for Stationarity and Structural Breaks in time-series
Before using the Johansen’s multivariate co-integration test, it is necessary that all
variables must be non-stationary or integrated of first order, I (1), in the levels and
stationary or I (0) in the first difference. Many unit root tests are available to examine
stationary properties of a time series; each test has high power only under certain
conditions. None of them is universally superior to the others. To obtain reliable
inference regarding the stationary properties of each time-series, three unit root tests are
used: the Augmented Dickey-Fuller (ADF) test, the Phillips-Perron (PP) test, and the
Zivot-Andrews unit root test. The ADF test has been the most commonly used unit root
test (Davidson and MacKinnon 2008). It provides information on whether the variable
under study has some deterministic terms in the regression, which facilitates the
specification of the VEC model. An assumption of the ADF test is that the error terms
follow an AR process of known order. However, when the error terms seem to follow an
MA or ARMA process, in which the moving average polynomial has a large negative
root, the ADF test has low power. Many alternatives to ADF tests have been proposed.
Among the best known are the tests proposed by Phillips and Perron (1988), also called
the PP tests. One of the critical aspects of the ADF and PP tests is a choice of lag length,
23
k, to eliminate autocorrelation in error terms, and the lag length is selected using Durbin-
Watson test (Wooldridge 2002). A modified ADF test known as Dickey-Fuller
generalized least squares (DF-GLS) de-trending procedure has been proposed by Elliott
et al. (1996), and this test has significantly greater power than the both ADF and PP tests.
In application of this test, we use Swartz minimum information criteria (SMIC) to select
the number of lags. Nevertheless, none of these three tests considers structural breaks that
might have occurred in the time-series. Perron (1989b) has shown that a unit root test that
does not take into account the break in the series will have low power. Thus, to verify the
validity of the ADF, PP and ADF-GLS tests, the Zivot-Andrews unit root test (Zivot and
Andrews 1992) is used to explore the possibility of structural breaks.
3.2.3 Lag length in the VEC Model
The VEC model estimation results are sensitive to the number of lags included in the
model. An inappropriate lag can distort the size of the test and results in loss of power
(Hafer and Sheehan 1991). The Akaike information criterion (AIC) is used to determine
the lag length in the model, which has been proved to outperform the other lag selection
criteria by Chueng and Lai (1993) and Lu¨tkepohl and Saikkonen (1999) using Monte
Carlo simulation.
3.2.4 Testing for Parameter Stability
One of the assumptions of the VEC model is that the parameters like the mean, variance,
and trend remain constant over time. However, if these parameters do not remain
constant over time, it is inferred that a structural break has occurred in the model. Tests
for these changes are known as stability condition tests. Lu¨tkepohl (1993) has suggested
the Eigenvalue test in a VEC model. The test provides an indicator of whether the
number of cointegrating equations is mis-specified or whether the cointegrating equations
are not stationary. If there are p endogenous variables and r cointegrating vectors, there
will be (p-r) unit moduli in the companion matrix and all other remaining moduli are
strictly less than 1, if the model satisfies the stability condition (STATA 2008).
All the estimations and tests in this chapter are performed using STATA/SE version 10.1
computer software.
24
3.3 Data Description
Daily price data for the econometric analysis for this chapter is taken from the European
Climate Exchange in Europe Union; from Chicago Climate Exchange, Regional
Greenhouse Gas Initiative and California Climate Action Registry in the USA; and from
Montreal Climate Exchange in Canada. Prices from European Climate Exchange are
available in Euros; from US exchanges in US Dollars; while those from Montreal
Climate Exchange are available in Canadian Dollars. Some transformations of the data
are carried out for analysis. To ensure compatibility between different prices, all prices
have been converted into US$ using daily exchange rates from Federal Reserve Statistical
Release (2010 and 2011). These carbon markets alongwith data sets are described in this
section.
3.3.1 European Climate Exchange (ECX)
European Climate Exchange (ECX) is the platform for carbon trading in European Union
(EU), in which two types of carbon credits (assets) are traded: EU allowances (EUAs)
and Certified Emission Reductions (CERs). Over 100 leading global businesses are
member of ECX emissions products. Trading on the ECX began in April 2005, with
launch of futures contracts. Data for the price series of futures market for both EUA and
CER are used in this chapter.
3.3.2 Chicago Climate Exchange (CCX)
Chicago Climate Exchange (CCX) is a voluntary, legally binding greenhouse gas
reduction and trading system for emission sources and offset projects in North America.
CCX employs independent verification, includes six greenhouse gases, and has been
trading greenhouse gas emission allowances since 2003. CCX has more than 350
members including corporations, educational institutions, and farmers and their
organizations. The commodity traded on CCX, is the Carbon Financial Instrument (CFI)
contract, each of which represents 100 metric tons of CO2 equivalents (CCX 2010). To
carry out empirical analysis, we use futures market prices for both allowances and CERs.
25
3.3.3 Regional Greenhouse Gas Initiative (RGGI)
The Regional Greenhouse Gas Initiative (RGGI) is the first mandatory, market-based
effort in the United States to reduce greenhouse gas emissions. Ten Northeastern and
Mid-Atlantic states have capped and decided to reduce 10% CO2 emissions from the
power sector by 2018. States sell nearly all emission allowances through auctions and
invest proceeds in consumer benefits: energy efficiency, renewable energy, and other
clean energy technologies. The initiative envisages spurring innovation in the clean
energy economy and creating green jobs in each state (RGGI 2010). Data for the price
series of futures market for allowance-based assets are used in this chapter. No CERs are
being traded in RGGI.
3.3.4 California Climate Action Registry (CCAR)
The California Climate Action Registry (CCAR) is a program of the Climate Action
Reserve and serves as a voluntary greenhouse gas (GHG) registry to protect and promote
early actions to reduce GHG emissions by organizations by developing and promoting
credible, accurate, and consistent GHG reporting standards and tools for organizations to
measure, monitor, third-party verify and reduce their GHG emissions consistently across
industry sectors and geographical borders. Its members voluntarily measure, verify, and
publicly report their GHG emissions, and are actively participating in solving the
challenge of climate change. The State of California offers its efforts to ensure that
California Registry members receive appropriate consideration for early actions in light
of future state, federal or international GHG regulatory programs (CCAR 2010). Data for
price series of futures market for allowance-based assets are used in this chapter. No
CERs are being traded in CCAR.
3.3.5 Montréal Climate Exchange (MCeX)
The Montréal Climate Exchange (MCeX) provides a market-based solution to help
reducing greenhouse gas (GHG) emissions in Canada. The mission of MCeX is to
provide a transparent and credible marketplace where contracts on GHG emissions are
exchanged. Montréal Climate Exchange is a joint venture between the Montréal
26
Exchange (MX) and the Chicago Climate Exchange (MCeX 2010). The data from MCeX
is available for futures allowances from May 2007 onwards.
In this chapter, daily price data from all the markets is taken for the period of August
2007 to December 2010. Data notations are described in Table 3.1 and the price series are
shown in Figure 3.1. From the figure, apparently nothing could be said about whether
different markets are integrated or not. However, the price dynamics seem to be similar
among assets within EU and among different assets within North America apart from the
two CER-based assets. However, the long-run and short-run integration is difficult to
infer from just graphical presentation.
Table 3.1. Data description for the price series of carbon markets in EU, USA and
Canada for both Allowance and CER based assets (credits)
Series Description
EUA Price of EU allowances
EUCER Price of EU certified emissions reductions
CCXIA Price of allowances in Chicago Climate Exchange
RGGIA Price of allowances in Regional Greenhouse Gas Initiative
CCXCER Price of certified emissions reductions in Chicago Climate Exchange
MONTLA Price of allowances in Montreal Climate Exchange
CCARA Price of allowances in California Climate Action Registry
27
CO2 Prices in different Carbon Markets
0.00
10.00
20.00
30.00
40.00
50.00
60.00
1 32 63 94 125 156 187 218 249 280 311 342 373 404 435 466 497 528 559 590 621
Time (Days)
Price (US$)
EUA EUCER CCXA RGGIA
CCXCER CCARA MontrealA
Figure 3.1. Allowance and CER asset prices in carbon markets of EU and North America
3.4 Results and Discussion
3.4.1 Results for Unit Root Tests
The results for unit root tests of ADF and Philips-Peron, for the 7 price series are given in
Table 3.2. Lag selection was made using the Durbin-Watson test. Null hypothesis of a
unit root in the univariate representation cannot be rejected for any of these 7 variables at
5% levels of significance, and each price series becomes stationary after first
differencing. Hence all 7 price series are I (1). The Results of DF-GLS unit-root tests
alongwith lags (selected through Schwert Information Criteria) are provided in Table 3.3
and the results confirm the results of ADF and PP tests that the price series are I(1) . The
results of Zivot-Andrews unit root test, which are also given in Table 3.3, indicate that
the properties of non-stationarity are not affected by structural breaks in any of these
price series, except CCARA, which has a structural break in March 2009. All these tests
are satisfied for all the carbon markets for both allowance and CER based assets. The
only exception is CCARA, which is therefore dropped out in further analysis. There could
be various reasons behind a structural break in CCARA. The State of California has been
quite active to the problem of Climate Change. Under California’s Climate Change
Program, emission reduction targets were set in 2005 and reporting of GHGs was made
28
mandatory in December 2007. Further, in December 2008, economy wide cap-and-trade
system was established, apart from implementing a regulation on electrical utilities that
33% of their electricity would be obtained from renewable sources of energy (Nichols
2009). Such policies of the Government in California might have been responsible for
introducing structural breaks in the time-series of prices in CCARA around March 2009.
Table 3.2. Results of ADF and Phillips-Perron unit root tests for carbon prices in the
markets of EU, USA and Canada
ADF Statistics Phillips – Perron Statistics
Z(rho) Z(t) Z(rho) Z(t)
Series Levels Differenced Levels Differenced
EUA -2.872 -43.8** -9.03 -2.11 -1271** -45.3**
EUCER -0.981 -46.8** -20.5 -3.4 -502** -42.6**
CCXA -1.485 -28.2** -5.4 -1.6 -634** -28.1**
RGGIA -2.251 -63.4** -5.6 -2.25 -379** -56.8**
CCXCER -2.611 -28.7** -9.75 -2.62 -315** -27.7**
CCARA -2.42 -31.1** -9.45 -2.22 -222** -36.4**
MONTLA -1.035 -47.3** -1.5 -1.0 -433** -46.6**
The symbol ** indicate 5% significance level
29
Table 3.3. Results of DF-GLS and Zivot-Andrews unit-root tests for carbon prices in the markets of EU, USA and Canada
Levels Differenced
Series lags DF-GLS lags DF-GLS Zivot-Andrews
EUA 3 -1.931 3 -14.3** -3.5
EUCER 1 -1.337 3 -3.19** -4.48
CCXA 1 -2.080 8 -3.21** -3.82
RGGIA 2 -2.043 2 -3.99** -4.39
CCXCER 1 -1.860 5 -3.01** -4.35
CCARA 1 -1.99 4 -11.6** -5.28**
MONTLA 1 -1.221 3 -3.5** -3.90
The symbol ** indicate 5% significance level
3.4.2 Carbon Market Integration at international level
Following Shahi, Kant and Yang (2006), the results of Akaike information criteria (AIC)
are used to determine the lag length. AIC chooses lag length j to minimize: log(SSR(j)/n)
+ (j + 1)C(n)/n, where SSR(j) is the sum or squared residuals for the VAR with j lags and
n is the number of observations; C(n) = 2 for AIC (Wooldridge 2002). In STATA 10,
there is a single command that calculates the number of lags, which comes out to be three
in our case.
Using a lag length of three is used for cointegration analysis; the results of Johansen’s
multivariate co-integration test for the number of cointegrating vectors in the 6-
dimensional system are given in Table 3.4. The trace statistics indicate that all six carbon
markets are not integrated.
30
Table 3.4. Results of Johansen’s multivariate co-integration tests for the carbon markets
of EU, USA and Canada for both Allowance and CER based credits of EUA, CCXA, RGGIA,
MONTLA, EUCER, and CCXCER (using 3 lags)
No. of co-integrating vectors Trace Statistics Critical value (5%)
r = 0 408.16** 94.15
r ≤ 1 184.51** 68.52
r ≤ 2 51.05* 47.21
r ≤ 3 20.73 29.68
r ≤ 4 6.65 15.41
r ≤ 5 0.65 3.76
The symbol ** indicate 5% significance level
In the next step, tests of co-integration are performed, taking five markets, at a time and
the results are shown in Table 3.5, which shows that even in the groups of five assets, the
markets are not co-integrated. Thenafter, the co-integration tests are performed by taking
four markets, at a time and Table 3.6 indicates the results. Maximum rank of 2 for the
four allowance-based assets (shown as bold letters in Table 3.6) depicts that even four
carbon markets of Allowance-based assets are not integrated. All these results, therefore
indicate that the LOP does not exist across the combined carbon markets of EU and
North America.
31
Table 3.5. Results of Johansen’s multivariate co-integration tests for carbon
markets of EU, USA and Canada for both Allowance and CER based credits of
EUA, CCXA, RGGIA, MONTLA, EUCER, and CCXCER, taking five assets at a time (using
3 lags)
Group of five assets, tested for co-integration Maximum Rank
CCXA, RGGIA, MONTLA, EUCER, and CCXCER 3
EUA, RGGIA, MONTLA, EUCER, and CCXCER 2
EUA, CCXA, MONTLA, EUCER, and CCXCER 2
EUA, CCXA, RGGIA, EUCER, and CCXCER 2
EUA, CCXA, RGGIA, MONTLA and CCXCER 1
EUA, CCXA, RGGIA, MONTLA, and EUCER 1
Table 3.6. Results of Johansen’s multivariate co-integration tests for carbon markets of EU,
USA and Canada for both Allowance and CER based credits of EUA, CCXA, RGGIA, MONTLA,
EUCER, and CCXCER, taking four assets at a time (using 3 lags)
Group of four assets,
tested for co-integration
Maximum Rank Group of four assets,
tested for co-integration
Maximum Rank
CCXA, MONTLA, EUCER, and
CCXCER
2 EUA, RGGIA, EUCER, and
CCXCER
1
CCXA, RGGIA, EUCER, and
CCXCER
1 EUA, CCXA, EUCER, and
CCXCER
1
CCXA, RGGIA, MONTLA,
and CCXCER
1 EUA, CCXA, RGGIA and
CCXCER
1
32
CCXA, RGGIA, MONTLA and
EUCER
2 EUA, CCXA, RGGIA and
EUCER
2
RGGIA, MONTLA, EUCER,
and CCXCER
2 CCXA, RGGIA, MONTLA
and CCXCER
1
EUA, MONTLA, EUCER, and
CCXCER
2 EUA, RGGIA, MONTLA and
CCXCER
2
EUA, RGGIA, EUCER, and
CCXCER
1 EUA, CCXA, MONTLA and
CCXCER
1
EUA, RGGIA, MONTLA, and
CCXCER
1 EUA, CCXA, RGGIA and
CCXCER
1
EUA, RGGIA, MONTLA, and
EUCER
2 EUA, CCXA, RGGIA and
MONTLA
2
CCXA, MONTLA, EUCER, and
CCXCER
2 CCXA, RGGIA, MONTLA,
and EUCER
1
EUA, MONTLA, EUCER, and
CCXCER
1 EUA, RGGIA, MONTLA, and
EUCER
1
EUA, CCXA, EUCER, and
CCXCER
2 EUA, CCXA, MONTLA, and
EUCER
2
EUA, CCXA, MONTLA and
CCXCER
1 EUA, CCXA, RGGIA and
EUCER
1
EUA, CCXA, MONTLA and
EUCER
1 EUA, CCXA, RGGIA and
MONTLA
2
Going a step further, the co-integration tests are performed by taking combinations of
three markets at a time. The results show that even in the groups of three, most markets
are not co-integrated. The only exceptions in this case are three allowance-based markets
of North America - CCXA, RGGIA and MONTLA are co-integrated, the results of which
are given in Table 3.7.
33
Table 3.7. Results of Johansen’s multivariate co-integration tests for only Allowance-
based credits of CCXA, RGGIA and MONTLA in North America only (using 3 lags)
No. of co-integrating vectors Trace Statistics Critical value (5%)
r = 0 30.12* 29.68
r ≤ 1 15.95* 15.41
r ≤ 2 4.77* 3.76
The stability of this VEC model for North American markets is tested using Lütekpohl
Eigenvalue stability tests, the results of which are shown in Figure 3.2. The VEC model
specification imposes 1 unit modulus, and the rest of the moduli are strictly less than 1.
Therefore VEC is stable for the three allowance-based assets of North American markets
and hence the results of cointegration test for North American markets are robust.
-1-.5
0.5
1Imaginary
-1 -.5 0 .5 1Real
The VECM specification imposes 1 unit modulus
Roots of the companion matrix
Figure 3.2. Graph of structural stability tests using Eigenvalue
stability condition in VEC model for Allowance-based assets
CCXA, RGGIA and MONTLA in North America
Lastly, the co-integration tests are performed by taking combinations of two assets at a
time. The results from these tests indicate that that most of the carbon markets are not co-
34
integrated in pairs. The only exceptions are the CER markets of EU and Chicago Climate
Exchange (EUCER, and CCXCER,) which are integrated. Hence, the results of Johansen’s
multivariate co-integration tests for CER-based credits only for both the markets of EU
and North America are given in Table 3.8.
Table 3.8. Results of Johansen’s multivariate co-integration tests for carbon markets of
EU and North America for CER-based credits EUCER and CCXCER (using 3 lags)
No. of co-integrating vectors Trace Statistics Critical value (5%)
r = 0 17.20* 15.41
r ≤ 1 7.09* 3.76
The stability of this VEC model for CER-based assets in carbon markets is also tested
using Lütekpohl Eigenvalue stability tests, the results of which are shown in Figure 3.3.
The VEC model specification imposes 1 unit modulus, and the rest of the moduli are
strictly less than 1. Therefore VEC is stable for the two allowance-based markets of the
EU and CCX, and hence the results of cointegration test these markets are robust.
In fact, the data for the two CER markets are available since 2005. Hence, for these two
markets Johansen’s cointegration test was also conducted for the entire period, and the
markets were found to be cointegrated during this entire period.
35
-1-.5
0.5
1Imaginary
-1 -.5 0 .5 1Real
The VECM specification imposes 1 unit modulus
Roots of the companion matrix
Figure 3.3. Graph of structural stability tests using Eigenvalue
stability condition in VEC model for CER-based assets
EUCER, and CCXCER in EU and North America
3.4.3 Long-run relationships of prices
The long-run relationship of prices among the co-integrated markets is defined by the
cointegrating vector β obtained from the Johansen cointegration test corresponding to the
highest Eigenvalues. The normalized coefficients α represent the weights or adjustment
coefficients that measure the average speed of adjustment toward the long-run
equilibrium, and a high value of α indicates rapid adjustment toward equilibrium
(Hänninen 1998). Since co-integration is observed among allowance-based North
American carbon markets; and also between CER-based EU and North American carbon
markets, the long-run relationships are compared among these two sets of co-integrated
markets. The long-run equilibrium relationship for allowance-based assets of North
American carbon markets CCXA, RGGIA and MONTLA is found to be:
RGGIA = 0.00005 CCXA – 0.75 MONTLA – 0.26 (3.4)
With the corresponding α values of weighting matrix as given below:
36
0.056 CCXA – 0.017 RGGIA + 0.037 MONTLA (3.5)
The β values in equation (3.4) indicate that in long-run equilibrium any increase in prices
in Chicago Climate Exchange will lead to a negligible increase in prices in Regional
Greenhouse Gas Initiative carbon market but an increase in prices in Montreal Climate
Exchange will have a significant negative effect on the prices in Regional Greenhouse
Gas Initiative market. In other words, in long-run equilibrium, a 1% increase in price of
allowances in RGGI market is accompanied by almost negligible price change in
allowance prices in CCX, keeping price in Montreal fixed; and a 1% increase in price of
allowances in RGGI market is accompanied by 0.75% decrease in prices of allowances-
based assets in Montreal Climate Exchange, keeping price in CCX fixed.
The values of α in weighting matrix (3.5) represent the speed of adjustment of each
variable toward the long-run equilibrium and measure the feedback effect of
disequilibrium in cointegrating relation on vectors in auto-regression. The coefficients in
weighting matrix show the slow adjustment of prices in RGGI towards long-run
equilibrium state, followed by Montreal exchange and fastest adjustment of prices in
Chicago Climate Exchange. The negative coefficient of RGGIA further implies that a
positive excess of long-run equilibrium induces a lower change in price of RGGIA (He,
Wang and Lai 2010).
Similarly, the long-run relationship defined by the cointegrating vector corresponding to
highest Eigenvalue for CER-based assets of EU and North American carbon markets
EUCER, and CCXCER is represented by
EUCER = 1.16 CCXCER – 35.9 (3.6)
With the corresponding α values of weighting matrix as
- 0.012 EUCER - 0.020 CCXCER (3.7)
The β values in equation (3.6) indicate that in long-run equilibrium, a 1% increase in
price of CERs in EU market is accompanied by 1.16% price increase in CER prices in
CCX, which indicates that the CER sellers in CCX are put in more advantageous position
37
as compared to their EU counterparts. However the values of α in weighting matrix (3.7)
show faster adjustment of prices of CER assets towards long-run equilibrium state in
Chicago Climate Exchange as compared to the EU market.
3.5 Summary and Conclusions
After the initiation of the EU Emission Trading Scheme (EU ETS) in 2005, several
carbon markets are now emerging world-wide, e.g. in the USA, Australia, New Zealand,
Canada, Japan and Switzerland. Integration of regional and international markets has
been proposed as one option to strengthen economic efficiency and politically reinforce
the international emissions trading regimes (for example Stern 2007, 2008; Edenhofer et
al. 2008; Garnaut 2008). The main objective of this chapter is to draw some inferences
for knowing market efficiency in carbon trading and linking different schemes and
markets, depending on the price dynamics in world’s carbon markets. In this chapter, the
Law of one price (LOP) is tested among different carbon markets of EU and North
America for both allowance and CER-based assets: CCXA, RGGIA, MONTLA, CCARTA,
EUCER and CCXCER using Johansen’s multivariate cointegration test.
The results indicate first of all that LOP does not exist as such among all the carbon
markets of EU and North America. This result is evident from all the cointegration tests
performed in this chapter, taking combinations of six, five and four assets at a time. Even
the CO2 allowance markets across the Atlantic are not integrated. This implies that the
effects of inter-continental allowance-based trade in carbon markets are limited; and thus
the market power of regional credit suppliers is large. This has particular implications for
the European carbon market, faced with a narrow oligopoly of suppliers, where strict
compliance may have weakened the bargaining power of the buyers. There could be
various reasons behind these results. First of all, allowance-prices in North America are
determined in a different manner from EU due to non-fixation of targets by the American
and Canadian Governments so far, than the prices in Kyoto compliant European Carbon
market. Carbon markets in North America are of voluntary nature so far. The agents
involved in these markets trade in carbon markets purely on account of their
environmental responsibility behavior, as contrasted to agents in EU markets, who are
mandated by law to fix emissions at a particular level. In addition, the Marrakesh
38
Accords allow only Kyoto signatory countries to use allowances from each other for
compliance purposes (Persson 2009) and EU Directive of 2003 makes clear that EU ETS
can be linked only with Kyoto compliance countries. Due to the fact that USA is not a
Kyoto-signatory so far, such link cannot be established and hence the two markets are not
cointegrated. Hence an overall inefficiency is introduced in the system and emissions
cannot be reduced at the least possible cost. An important policy intervention could be to
allow establishing links between different countries, irrespective of their Kyoto
commitments, so as to find a minimum cost solution to tackle climate change.
Second, a strong evidence for the regional market integration for allowance-based assets
is found in North American carbon markets. It shows a presence of regional effect in
North American carbon markets. The phenomenon could be possibly due to spatial
proximity of the markets with each other. In addition, the existence of cointegration
among the markets implies a common stochastic trend in those markets (Kasa, 1992; Jang
and Sul, 2002). Since each North American allowance market price series contains
information on the common stochastic trends (which bind all these markets together), the
predictability of one carbon market’s prices can be enhanced significantly by utilizing
information on the other market’s prices. The presence of common stochastic trends
among all these markets implies that once new information on carbon price in one market
is available prior to other markets’ prices, the other markets’ prices will deviate from that
trend through a transitory component (Masih & Masih, 1999). As traders in all these
markets have perfect information about all these markets, their transaction costs become
equal for trading in either of them.
Third, in the co-integrating vector of North-American markets, the coefficient of
Montreal Exchange prices is negative while the coefficients of the two US markets are
positive. This may be an indication of switching of some buyers, specifically Canadian
buyers, from the US markets to the Canadian market. In the beginning, when the
Montreal exchange was not established, the Canadian firms were trading in Chicago
exchange, and after the establishment of Montreal exchange these firms have an option to
trade either in the Canadian or US markets. Hence, the total demand is divided between
these two markets. In the long-run equilibrium, therefore, if more firms trade in the US
39
markets (which means increase in prices in the US markets), the Canadian market will
face less demand and therefore prices will decrease or vice-versa.
Fourth, a very striking finding of this chapter is that the Certified Emission Reduction
(CER) markets in Europe and USA are integrated. This could be explained by the fact
that the CER credits are generated mainly by the Clean Development Mechanism (CDM)
projects, primarily in the developing countries and irrespective of the trading countries;
their prices show co-movement around the world. It also indicates the efficiency of CDM
projects and existence of a global market for CDM under the overall carbon trading
process. However, there is a world of caution for the future. The types of projects
qualifying for availing CERs in Europe and in Chicago market are not similar. For
example, offsets generated from Forestry sector qualify in CCX, but not in EU market for
compliance purposes (ECX 2009 and CCX 2009). So situation in CER market might
change in future, if attempts are not made either to link or to make both the markets
homogenous with respect to type of projects. Nonetheless, the development of global
carbon market for CDM can be seen as one manifestation of improved expectations for
ensuring carbon sequestration and sustainable development in developing countries. To
confirm these expectations, the Annex-I countries should continue to improve the
investment environment and enhance incentives for these projects in the developing
world.
Fifth, these findings also indicate that most likely new carbon markets created in different
parts of the world such as Australia, Singapore, and other countries, will not be co-
integrated because each of these markets will be governed by a different set of
institutional arrangements and there will be restrictions on participation of buyers from
other countries and regions. The possibilities of arbitrage across the global markets will
be limited, and the carbon trading in these markets will be globally inefficient. Hence,
there is a strong need of a global agreement that allows global carbon trade to prevent
climate change at the least cost options.
Finally, this chapter is a first attempt on exploring integration of carbon markets using
price dynamics. Inspite of the new findings, the study, however, is not free from various
40
limitations. For example, the number of co-integrated markets is not a true measure of the
degree of market integration; that can be only assessed by measuring the reaction time to
remove disequilibria from the cointegrating relationships. Similarly, Johansen’s
multivariate cointegration procedure does not take into account the transaction costs, the
marginal abatement costs and other charges associated with carbon trading; and therefore
is not a very reliable method for analyzing the efficiency of arbitrage between the two
markets. In addition, only univariate price equations have been considered, whereas,
volume of trading can also be taken into account while exploring market integration.
Future research should include more assets from other carbon markets of the world and
the enhanced aspects of market integration. New research should not only confirm or
contradict the present results, but also try to resolve such issues by using further
econometric analysis and looking at more recent developments in the international carbon
markets using more extensive data series coming from newly emerging carbon markets.
41
4 Forecasting volatility of carbon markets
ABSTRACT
Market volatility plays a big role for investments in carbon portfolios and can be an
important input into macro-econometric models and calculation of value-at-risk. This
chapter evaluates the performance of various econometric models, both simple and
complex, for predicting short-term price volatility in European Climate Exchange (ECX)
and Chicago Climate Exchange (ECX). Despite various policy level changes in emission
trading mechanisms, volatility in the two carbon markets follows a stationary pattern and
hence can be forecasted. Voluntary carbon market of CCX is relatively more volatile and
is forecasted best by complex model like non-linear GARCH; and the behavior of this
voluntary market is similar to that found in other financial markets and energy markets.
The compliance market of ECX, on the other hand, is less volatile and is forecasted best
by simple econometric models like Historical Averages and GARCH (1, 1) and hence is
different from both compliance markets and other financial markets. Findings of this
chapter could be useful in making decisions in carbon portfolio investments by
individuals and firms; and for making choice between various policy instruments at the
strategic level.
Key words: carbon market; climate change; price; volatility; forecasting; econometric
model
4.1 Introduction
Carbon markets around the world have witnessed a big growth in the recent past. The
markets continue to grow year after year, reaching about US$ 122 Billion in 2009, which
is over 12 times their 2005 value (World Bank 2010). This new market system represents
a shift in paradigms, since environmental policy has historically been a command-and-
control type regulation where companies are required to comply with emission standards
or implement particular technologies. At the recent Copenhagen and Cancun meets of the
United Nations Framework Convention on Climate Change (UNFCCC), it has been
decided by the international community to pursue carbon market approach to enhance the
42
cost-effectiveness and to promote mitigation actions for curbing climate change (CoP,
2010). There are two major types of carbon markets: compliance (or regulatory) markets
and voluntary markets. Compliance markets are created and regulated by mandatory
regional, national, and international carbon reduction regimes. Voluntary carbon markets
function outside of the compliance markets, enabling companies and individuals to
purchase carbon offsets on a voluntary basis. A voluntary market reflects the sum of all
transactions of carbon credits and allowances, where the final purpose of cancelling or
retiring the carbon credit is not to comply with legislation or to fulfill agreements
between companies and governments (Capoor and Ambrosi 2009).
Due to establishment of carbon markets, the right to emit a particular amount of carbon
dioxide (CO2) has become a tradable commodity. By requiring the emitters to hold an
adequate stock of allowances that corresponds to their CO2 output, carbon markets
provide new business development opportunities for market intermediaries and service
providers. The price behavior and dynamics of this new asset class, the carbon credits,
has acquired a lot of importance (Benz and Trück 2009). Risk management consultants,
brokers, carbon procurement funds and hedge fund managers and other buyers are
scouring the globe for opportunities to buy carbon credits (Labbat and White 2009).
Despite their voluminous growth, carbon markets, however, have experienced a lot of
fluctuations since their very inception, which are caused by the market uncertainties.
Because supply, demand, and regulatory conditions evolve unpredictably over time,
regulations based on fixing emission levels are causing a lot of volatility in market price
of carbon. The history of European trading prices for CO2 illustrates the extreme
volatility of carbon markets, for example during 2006 itself, the range of trading prices
varied from $44.47 to $143.06 per ton carbon (Capoor and Ambrosi 2009). Therefore a
lot of insight could be gained by looking into the functioning of carbon markets by
examining their historical volatility.
Volatility measures the average absolute daily change, and is a common approach to
indicate the variability and unpredictability of the price of a tradable commodity
(Nordhaus 2007). For carbon markets, in particular, a full understanding of volatility of
carbon prices is critical from multiple perspectives. First, price volatility could
43
discourage the deployment of new capital intensive abatement technologies, by giving
rise to an option value from delaying irreversible investments (Chao and Wilson 1993).
Second, for most of the investment decisions, volatility shall determine the return on
capital. For example for an electric utility deciding whether to install carbon capture and
storage (CCS) technology, the return from initial capital cost of CCS will depend on the
expected variable costs of capturing and storing carbon, relative to reducing emissions by
fuel-switching or demand-side management. Third, price volatility may have some major
disruptive effects on the price dynamics of the market. For stability, it is imperative to
limit price volatility by allowing banking or borrowing of carbon credits for future use,
setting price floors and ceilings or linking various carbon trading schemes together
(Brohe et. al. 2009, 51-53). Lastly, forecasts of carbon price volatility could be important
inputs into macro-econometric models and market risk assessment calculations. Price
volatility, therefore, is one of the key factors in the choice of a carbon policy instrument.
Recently, a large volume of literature has emerged on modeling and forecasting volatility
in financial markets. Most of this research has focused on equity or foreign exchange
markets (for example, Bollerslev 1986; Akgiray 1989; Pagan and Schwert 1990;
Brailsford and Faff 1996; Yu 2002; Brooks and Persand 2002, 2003). A general
consensus from this literature is that generalized autoregressive conditional
heteroskedastic (GARCH) models and their variants tend to work better, over different
series and data frequencies, as compared to other techniques like moving average,
exponential smoothing and linear regression for such markets. Kang, Kang and Yoon
(2009) investigate the efficacy of volatility forecasting models for three crude oil
markets, and found advanced GARCH models more useful. Sadorsky (2006) also proves
the same for heating oil and natural gas volatility. For carbon markets, most of research is
focused on modeling price behavior rather than volatility. Benz and Trück (2009) analyze
the short-term price behavior of carbon dioxide (CO2) emission allowances of the EU
emissions trading system (EU ETS). They suggest the use of Markov switching and AR–
GARCH models for stochastic price modeling. Seifert, Uhrig- Homburg and Wagner
(2008) investigate the success chances and optimal design of derivatives on emission
allowances and develop a stochastic equilibrium model reflecting in a stylized way the
most important features of the EU ETS and analyze the resulting price dynamics. Their
44
main findings are that an adequate CO2 process does not necessarily have to follow any
seasonal patterns. Paolella and Taschini (2006) provide an econometric analysis
addressing the unconditional tail behavior and the heteroskedastic dynamics in the returns
on CO2 and SO2 allowances. Daskalakis, Psychoyios and Markellos (2005), in their study
on emission allowance prices and derivatives, argue that market participants adopt
standard no-arbitrage pricing. A major gap in this carbon market literature is that all these
studies focus primarily on the European carbon market and even for that the specific
focus is on price, rather than volatility.
In this chapter, out-of-sample performance of various econometric models is assessed for
forecasting volatility in carbon markets of European Climate Exchange (ECX) and
Chicago Climate Exchange (CCX). Volatility forecasts are evaluated using different
approaches. The purpose is to compare the performance of eight econometric models
with regard to their ability to identify and forecast the price volatility in both compliance
and voluntary markets. The chapter contributes to the existing literature in three major
aspects. First, both compliance market of ECX and voluntary market of CCX have been
studied, thus expanding the sphere of research which had been primarily focused on ECX
so far. Second, future and option markets of carbon are also studied in addition to spot
markets. Since futures and options rather than spot prices are likely to be held for
investment purposes (Daskalkis, Psychoyios and Markellos 2009), it becomes all the
more important to carry out their study. Finally, instead of concentrating just on the price
of carbon credits, the primary objective of this chapter is to forecast volatility.
The chapter is organized as follows. Section 4.2 describes the theory of volatility in
carbon markets. Section 4.3 outlines the econometric models used in this paper for
volatility forecasts. Tests for stationarity and structural breaks are described in section
4.4. Evaluation measures used to assess the performance of the candidate models are
presented in Section 4.5. Section 4.6 describes the data set used in this chapter. Section
4.7 describes the empirical results and Section 4.8 gives summary and conclusions.
45
4.2 Volatility in carbon markets
Following an approach similar to that of Burtraw (1996), the principle driving factors of
volatility in carbon market prices can be categorized into (i) policy and regulatory issues
and (ii) market fundamentals that directly concern the production of CO2 and thus
demand and supply of carbon credits. Changes in policy directives or regulations may
have substantial consequences on the long-term price behavior of market volatility. In the
carbon market these could be decisions and announcements concerning allowance
allocation plans or change of national emission caps. Hence, the consequences of changes
in such regulatory or policy issues may be sudden price jumps, spikes or phases of
extreme volatility in allowance prices. For example, long-run volatility in the EU ETS in
2006–2007, during the program’s pilot phase, arose from an oversupply of allowances
along with the failure to allow banking (Keohane 2009). However, we have not
incorporated long-run volatility in our econometric models, as focus of this chapter is
only on the short-term volatility behavior, which is affected by market fundamentals that
directly concern the production of CO2 and thus demand and supply of carbon credits. It
could also be affected by certain design features and trends in other carbon markets (Benz
and Trück 2006). It is the challenge of an appropriate stochastic model, therefore, to
capture short-run volatility patterns in carbon markets. The most common measure of a
short-term volatility is daily market volatility. In the literature there are a number of ways
to obtain daily volatility series. The daily returns on day t are defined as the natural
logarithm of price relatives (Merton 1980 and Perry 1982); that is
1
log−
=t
tt
P
Pr (4.1)
where tP is the daily price of Carbon in any of these markets. The daily market volatility
is defined as the squared daily returns (Sadorsky 2006), that is, Daily Volatility
22
tT r=σ (4.2)
46
4.3 Econometric Models used to test Volatility
We use eight models for the purpose of forecasting the above described daily volatility of
carbon markets.
4.3.1 Random Walk
The random walk model is the simplest possible econometric model and is defined as
22
1ˆ
tt σσ =+ (4.3)
hence it is assumed that the best forecast of next day’s volatility is today’s volatility.
4.3.2 Historical average
If the conditional expectation of volatility is assumed to be constant, the optimum
forecast of future volatility would be the historical average, that is
2
1
2
1 /1ˆt
T
tt T σσ ∑ =+ = (4.4)
Here T is the number of days since beginning of trading of a particular carbon asset. This
is the model used most often in the past to predict volatility.
4.3.3 Moving averages
According to the historical average model, all past observations receive equal weight. In
the moving average model, however, more recent observations receive weight. In this
chapter, a 400-day moving average model is used. The model is defined as
2
1
400
1
2
1 400/1ˆjtjt −+=+ ∑= σσ (4.5)
4.3.4 OLS regression
This is one-step ahead forecast based on the simple OLS regression of the volatility on
day t+1 on the volatility at day t. The expression is given by
2
21
2
1ˆ
tt σββσ +=+ (4.6)
47
4.3.5 Autoregressive conditional heteroskedasticity (ARCH)
The basic idea of ARCH models (Engle 1982) is that the square of the error term at time t
depends on the realized values of the squared error terms in previous time periods
(Davidson and McKinnon 2004). The model ARCH (q) is defined by
tttr εσ= ; ∑=
−− +=Ω≡q
i
itittt uuE1
2
01
22 )( αασ (4.7)
where αi > 0 for all i=0,1,……….., q. Here εt is white noise with variance 1 and q is the
previous time-periods to be considered for error terms. Here, analysis is done for ARCH
(1) model. Using first observations, the parameters α0 and α1 are calculated and then daily
volatility forecast for 2
tσ is calculated using
2
110
2 ˆˆ−+= tt rαασ (4.8)
4.3.6 Generalized autoregressive conditional heteroskedasticity (GARCH)
A major drawback of ARCH models is that they do not consider the dependence of
variance on the variance of previous time-periods. Hence generalized ARCH model,
proposed by Bollersev (1986), is used instead of the original ARCH model (Davidson
and McKinnon 2004). GARCH (p, q) process is defined as
tttr εσ= ; ∑∑ = −
=
−− ++=Ω≡p
j jtj
q
i
itittt uuE1
2
1
2
01
22 )( σδαασ (4.9)
where 1⟨+ δα and δj > 0 for all j=0,1,….p. Here p is the previous time-periods to be
considered for variance. GARCH (1, 1) model has been found to be adequate in many
applications (Yu 2002) and hence is used here as a candidate model. In this model, first
the parameters α0, α1 and δ1 are estimated and then daily volatility forecast for 2
tσ is
estimated using
2
11
2
110
2 ˆˆ−− ++= ttt u σδαασ (4.10)
48
4.3.7 Asymmetric GARCH
Asymmetric GARCH models (Hentschel 1995) incorporate the asymmetric impacts of
shocks or news of equal magnitude but opposite sign on the conditional variance of asset
returns. Various asymmetric GARCH models are available. Quadratic-GARCH model, of
Sentana (1995) has been used here, which is defined as
tttr εσ= ; ∑∑∑ = −= −
=
−− +++=Ω≡q
i iti
p
j jtj
q
i
itittt uuuE11
2
1
2
01
22 )( ωσλαασ (4.11)
With respect to the simpler GARCH(1,1) model, only the term ut-1 is added, which allows
for the asymmetric impact of positive and negative shocks. The asymmetry of the impact
varies as the dimension of the shock varies; in particular the asymmetric impact decreases
as the dimension of the shock increases. If ω is negative, the impact of negative shocks is
larger than the impact of positive shocks. Since the index of kurtosis for ut is a positive
function of the module of ω, this asymmetric-GARCH model is able to rationalize excess
kurtosis in returns coming from investments in carbon markets. Like in GARCH (1, 1)
model, first the parameters α0, α1 and λ1 and ω1 are estimated and then daily volatility
forecast for 2
tσ is esimated using
tttt uu 1
2
11
2
110
2 ˆˆ ωσλαασ +++= −− (4.12)
4.3.8 Non-linear GARCH
In practice the simple GARCH (1, 1) model has been by far the most commonly used
model for conditional variance. However, in many cases it has been found that estimates
obtained for the parameters α and δ are such that their sum is relatively close to unity and
hence the stationarity condition α + δ < 1 is nearly violated. Models of this kind are often
undesirable because they can exaggerate volatility persistence and, consequently, result in
relatively poor volatility forecasts. Therefore, we shall consider nonlinear alternatives of
the conventional GARCH model, such as N-GARCH (1, 1), which is given below:
tttr εσ= ; 2
11
2
111
2
1101
22 )()( −−−− +++=Ω≡ tttttt HuuE σδσβαασ (4.13)
49
Where α1>0 and H1 is increasing function. In applications the function H1 depends on
parameters and it is supposed to be similar to the cumulative distribution function of a
positive continuous random variable. In this chapter, this is taken as a second order
quadratic function.
4.4 Testing for Stationarity and Structural Breaks
Before testing for complex econometric models like ARCH, GARCH and non-linear
models it is necessary that volatility variable must be stationary (Yu 2002). Many unit
root tests are available to examine stationary properties of a time series; each test has
high power only under certain conditions and none of them is universally superior to the
others. To obtain reliable inference regarding the stationary properties of each time-
series, we use three unit root tests: the Augmented Dickey-Fuller (ADF) test, the Phillips-
Perron (PP) test, and the Zivot-Andrews unit root test. The ADF test has been the most
commonly used unit root test (Davidson and MacKinnon 2004). An assumption of the
ADF test is that the error terms follow an AR process of known order. However, when
the error terms seem to follow an MA or ARMA process, in which the moving average
polynomial has a large negative root, the ADF test has low power (Schwert 1989). An
alternative to ADF is the test proposed by Phillips and Perron (1988), also called the PP
test. One of the critical aspects of the ADF and PP tests is a choice of lag length, k, to
eliminate autocorrelation in error terms, and in this study Durbin-Watson test
(Wooldridge 2002) is used to select the lag length. A modified ADF test known as
Dickey-Fuller generalized least squares (DF-GLS) de-trending procedure has been
proposed by Elliott et al. (1996), and this test has significantly greater power than the
both ADF and PP tests. In application of this test, Swartz minimum information criterion
(SMIC) is used to select the number of lags. Nevertheless, none of these three tests
considers structural breaks that might have occurred in the time-series. Perron (1989b)
has shown that a unit root test that does not take into account the break in the series will
have low power. Thus, to verify the validity of the ADF, PP and ADF-GLS tests, the
Zivot-Andrews unit root test (Zivot and Andrews 1992) is used to explore the possibility
of structural breaks.
50
4.5 Evaluation Measures
Three measures are used to evaluate the forecast accuracy. In addition to common
assessment measure as the Root Mean Square Error (RMSE) two other measures: the
Theil-U statistic and the LINEX loss function are also employed to evaluate the forecast
accuracy. The additional advantage of using Theil-U statistic is that it is invariant to any
linear transformation (Armstrong and Fildes 1995). The LINEX loss function has an
additional advantage that it is asymmetric and hence can evaluate positive errors more (or
less) than negative errors (Christofferson and Diebold 1987). Another reason for the
popularity of LINEX function is that it provides the analytical solution for the optimal
prediction under conditional normality (Yu 2002). The evaluation measures are defined
as
4.5.1 Root mean square error (RMSE)
RMSE = ∑=
−I
i
iiI 1
222 )ˆ(1
σσ (4.14)
4.5.2 Theil-U statistic
Theil-U = 22
1
2
1
1
222
)(
)ˆ(
i
I
i
i
I
i
ii
σσ
σσ
−
−
∑
∑
−
−
= (4.15)
4.5.3 LINEX loss function
LINEX = ]1)ˆ()ˆ([exp1 2222
1
−−+−−∑=
iiii
I
i
aaI
σσσσ (4.16)
Where a in the LINEX loss function is a given parameter. In the LINEX loss function,
positive errors are weighed differently from the negative errors. If a>0, the LINEX loss
function is almost linear for 0ˆ 22 >− tt σσ (over-predictions) and exponential for
0ˆ 22 <− tt σσ (under-predictions). Thus negative errors receive more weight than the
positive errors. In the context of volatility forecasts, this implies that an under-prediction
51
of volatility needs to be taken into consideration more seriously (Yu 2002). Similarly,
negative errors receive less weight than positive errors when a<0. In this chapter, two
values of a are used, namely, 20, and -20.
4.6 Data
For the compliance carbon market, data has been taken from the European Climate
Exchange (ECX), which is the trading platform for EU ETS. The ECX is the leading
market for trading CO2 emissions in Europe that allows the EU allowances (EUAs)
trading for spot, futures and options markets. Volatility study for the spot market of the
ECX has already been done by Benz and Trück (2009), and therefore this chapter focuses
on the futures and options markets only. For the ECX futures market, the data sample
consists of daily returns over the period from March 2006 to July 2009. The data for the
ECX Options market consists of daily returns over the period from October 2006 to July
2009. The data for voluntary market is taken from the Chicago Climate Exchange (CCX),
which is North America’s only voluntary market for offset projects. The CCX employs
independent verification, includes six greenhouse gases, and has been trading greenhouse
gas emission allowances since 2003. The commodity traded on CCX is the Carbon
Financial Instrument (CFI) contract, each of which represents 100 metric tons of CO2
equivalents. The CFI contracts are comprised of Exchange Allowances and Exchange
Offsets. Exchange Allowances are issued to emitting members in accordance with their
emission baseline and the CCX Emission Reduction Schedule. Exchange Offsets are
generated by qualifying offset projects (CCX 2010). To draw comparison with the
results of the EU spot market from Benz and Trück (2009), this chapter focuses on only
spot market of the CCX. The CCX data consists of daily returns over the period from
December 2003 to July 2009.
4.7 Results
The results of our analysis are divided into graphical analysis, stationarity analysis, and
volatility analysis and are given subsequently.
52
4.7.1 Graphical analysis
For the ECX Options market, the daily carbon prices are plotted in Figure 4.1, and daily
price volatility in Figure 4.2. From figure 4.2, we can observe that the ECX Options
market remained stable from its beginning in October 2006 to June 2008 and then
became volatile from July 2008 to July 2009. The increase in volatility after 2008 might
be due to beginning of the first commitment period of the Kyoto Protocol (2008-2012).
Fig.4.1. Price in ECX Options Market,
Oct. 2006 to Jul. 2009
Fig.4.2. Volatility in ECX Options
Market, Oct. 2006 to Jul. 2009
For the ECX Futures market, the daily carbon prices are plotted in Figure 4.3 and daily
volatility in Figure 4.4.
Fig.4.3. Price in ECX Futures Market,
Mar. 2006 to Jul. 2009
Fig.4.4. Volatility in ECX Futures Market,
Mar. 2006 to Jul. 2009
53
It is apparent from comparison of figures 4.2 and 4.4 that the trends of volatility in the
ECX Futures market were quite different from the ECX Options market.
Looking at the data from Chicago Climate Exchange (CCX), which is a voluntary
market, we have volatility data from December 2003 to July 2009. The daily variation of
the carbon price is plotted in Fig. 4.5 and the corresponding volatility in Fig. 4.6.
Fig.4.5. Price in CCX, Dec. 2003 to Jul.
2009
Fig.4.6. Volatility in CCX, Dec. 2003 to
Jul. 2009
From figure 4.6, it is apparent that ups and downs in the volatility of the CCX spot
market are altogether different from the ECX market. Apparently, there are three periods
of distinct volatility. CCX spot market remained highly volatile from December 2003 to
April 2006, possibly because it was a new market and then again volatility was high from
January 2008 to July 2009. In between these two periods, market was more or less stable.
Though the graphical analysis tells us about different volatility patterns, it does not
extend any help for the purpose of forecasting volatility in these markets. Hence we need
to look at the mathematical models to serve this purpose. But before doing that it is
necessary to see if these volatility series are stationary or are having structural breaks, as
depicted by graphical analysis.
4.7.2 Stationarity analysis
The above preliminary analysis of short-term volatility in the two carbon markets of ECX
and CCX shows that the nature of volatility in different markets is different and hence
54
needs different econometric models to explain. Before modelling such volatility for these
markets, we shall first have a look at the summary statistics of our data samples. Table
4.1 shows the mean, median, maximum, kurtosis and first four autocorrelations ρ1, ρ2, ρ3
and ρ4 of the entire sample for different carbon markets. The mean and median values of
volatility depict that CCX market remained more volatile as compared to its European
counterparts. Kurtosis values are very high for all the markets, which mean that the
unconditional distribution of volatility is not a normal distribution. Table 4.1 shows that
for all these markets, while higher order autocorrelations are in general diminishing, the
first autocorrelation is low but not negligible.
Table 4.1. Summary statistics of the volatility series and tests for non-stationarity for ECX and CCX
Carbon
Asset Mean Median Maximum Kurtosis ρ1 ρ2 ρ3 ρ4
ADF
Statistic
Philips- Peron
Statistic
z(rho) z(t)
ECX Options Market
.00075 .00091 0.069 119.95 0.554 0.031 0.024 0.029
-15.52* -398.9# -16.1†
ECX Futures Market
Future
Dec-09 .00087 .00018 0.079 382.39 0.66 0.015 .034 .0098 -27.50* -976.2# -28.2†
CCX Spot Market
Vintage
2003 .00174 .0021 0.065 38.57 0.471 .077 .022 .086 -30.62* -1289# -31.4†
*Critical value at 5% significance level is -3.5
# Critical value at 5% significance level is -4.245
† Critical value at 5% significance level is -3.49
55
This is the evidence of volatility clustering and suggests that volatility is predictable (Yu
2002). To test for the presence of unit roots, two tests, namely the Augmented Dickey-
Fuller (ADF) test and Philip-Peron (PP) test were performed. Corresponding statistics
were calculated and the results for ADF and PP are also presented in the last two columns
of Table 4.1. Both the tests confirm that the volatility series for the ECX Options and
Futures markets and the CCX spot market are stationary. The Results of DF-GLS unit-
root tests alongwith lags (selected through Schwert Information Criteria) are provided in
Table 4.2 and the results confirm the results of ADF and PP tests that the price series are
stationary. From graphical analysis these series were appearing to have structural breaks,
for which Zivot-Andrews test is carried out. The results given in Table 4.2 indicate that
any of these time series are not affected by structural breaks.
Table 4.2. Results of DF-GLS and Zivot-Andrews unit-root tests for carbon prices in ECX and CCX
Market of Carbon asset
lags DF-GLS Zivot-Andrews†
ECX Options
Market
2 -32.64* -2.5
ECX Futures
Market
1 -11.27* -3.3
CCX Spot
Market
1 -24.03* -3.25
*Critical value at 5% significance level is -3.19
†Critical value at 5% significance level is -5.08
4.7.3 Volatility analysis
First of all, a period has to be chosen for estimating parameters and a period for
predicting volatility. As the sample is rolled over, the models are re-estimated and ahead
daily forecasts are made. For all the three markets, 70% of the sample is used for
modeling the series and rest 30% is used for forecasting. The main results for the ECX
options market are presented in Table 4.3; for ECX futures market in Table 4.4; and for
CCX, Spot market in Table 4.5. The value and ranking of all eight competing models
56
under the RMSE, and Theil-U are reported. The same models are evaluated under
asymmetric loss functions, where two LINEX loss functions are used (a = 20, and -20).
Table 4.3. Results for performance of econometric models for ECX Options Market
RMSE Theil-U LINEX (a=20) LINEX (a=-20)
Value Rank Value Rank Value Rank Value Rank
Random Walk 0.0148 2 1.00 2 0.045 2 0.0426 2
Historical Averages 0.1136 6 59.00 6 1.3659 6 6.623 6
Moving Averages 0.0422 4 8.14 4 0.2011 4 0.9164 4
OLS 0.0705 5 22.77 5 0.6477 5 1.7388 5
ARCH(1) 0.5717 8 1494 8 10.432 7 94.75 8
GARCH (1) 0.0145 1 0.9712 1 0.0409 1 0.042 1
Asymmetric
GARCH (1,1) 0.2352 7 234.6 7 27.67 8 19.67 7
NLGARCH (1,1) 0.016 3 1.1805 3 0.0647 3 0.046 3
For ECX options market, the RMSE, Theil-U and LINEX statistics, as given in Table 4.3,
indicate that the simple GARCH (1, 1) model provides the most accurate forecasts while
the random walk ranks second. ARCH model ranks the last and hence is not a very good
method to forecast volatility of ECX options market. These findings pertaining to the
ECX options market are consistent with the findings of ECX, Spot market (Benz and
Trück 2009) where price volatility is also described most accurately by simple GARCH
models.
57
Table 4.4. Results for performance of econometric models for ECX Futures Market
RMSE Theil-U LINEX (a=20) LINEX (a=-20)
Value Rank Value Rank Value Rank Value Rank
Random Walk 0.0019 3 1 3 0.0008 3 0.0743 4
Historical Averages 0.0017 1 0.7912 1 0.0006 1 0.0566 1
Moving Averages 0.0018 2 0.8237 2 0.0007 2 0.0589 2
OLS 0.0071 5 13.4467 5 0.0095 5 1.0569 5
ARCH(1) 0.0297 8 235.6167 8 0.1028 8 0.2216 8
GARCH (1) 0.0217 6 126.2557 6 0.0621 6 8.6513 6
Asymmetric
GARCH (1,1) 0.0020 4 1.03383 4 0.0009 4 0.0738 3
NLGARCH(1,1) 0.0239 7 153.0988 7 0.0828 7 9.0397 7
Table 4.4 shows that for ECX futures market, all the measures of evaluation indicate that
the historical averages model provides the most accurate forecasts while the moving
averages ranks second for all the futures. Here also ARCH is not a very good method to
forecast volatility. This result of ECX futures market, contrasts not only with spot and
options markets of ECX, which are dominated by GARCH (1, 1) model, but also with
other futures markets like petroleum futures (Sadorsky 2006) and crude oil futures
(Moshiri and Foroutan 2006), for which volatility is described best by TGARCH model
and Non-linear GARCH models, respectively.
For the compliance market of ECX, in general, simple econometric models like the
historical averages and simple GARCH perform better than complex models for
forecasting purposes. This behavior of ECX is well contrasted with volatility of other
financial markets and energy markets for both spot trading and options and futures
stocks.
58
Table 4.5. Results for performance of econometric models for CCX, Spot Market
RMSE Theil-U LINEX (a=20) LINEX (a=-20)
Value Rank Value Rank Value Rank Value Rank
Random Walk 0.0099 7 1 7 0.0198 7 0.0192 7
Historical
Averages 0.0090 5 0.6947 5 0.0164 5 0.0104 5
Moving Averages 0.0083 4 0.6866 4 0.0162 4 0.0103 4
OLS 0.0080 3 0.6698 3 0.0156 3 0.0100 3
ARCH(1) 0.0110 8 1.3314 8 0.0229 8 0.0286 8
GARCH (1,1) 0.0095 6 0.7944 6 0.0188 6 0.0159 6
Asymmetric
GARCH (1,1) 0.0077 2 0.6339 2 0.014 2 0.0099 2
NLGARCH (1,1) 0.0076 1 0.0037 1 0.0016 1 0.0050 1
From Table 4.5, it is evident that the results for CCX, spot market are quite contrasting as
compared to the ECX markets. A prominent feature of Chicago Climate exchange is the
dominance of non-linear model NLGARCH (1, 1) for forecasting. Here also the ARCH is
not a very good method to forecast volatility of CCX, thereby confirming the result of
worst performance of ARCH (1) in ECX also. Non-linear GARCH models perform quite
well overall for forecasting purposes in the case of Chicago Climate Exchange. This
characteristic of the spot market of CCX also contrasts with ECX, Spot market (Benz and
Trück 2009) and ECX, options market, which also are forecasted the best by GARCH
type of models; and also with ECX, futures market, which is forecasted well by a simple
econometric model of historical averages. However, the behavior of CCX, spot market is
similar to other financial markets like, for example, New Zealand (Yu 2002), Asian stock
markets (Michelfelder 2005), European stock markets (Balaban, Bayar and Faff 2006)
and German DAX index (Kaufman and Scheicher 2006); and energy markets like, for
59
example, oil (Kang, Kang and Yoon 2008) and petroleum futures (Sardosky 2006), for
which the volatility is described best by the non-linear GARCH models.
Volatility analysis therefore shows that the volatility in voluntary market of CCX follows
the same pattern as the volatility in other financial markets and energy markets; whereas,
the patterns of volatility in the compliance market of ECX is different from such markets.
To understand the meaning of best performing models, it would be appropriate at this
stage to have a look at the coefficients of such models. Using STATA software, the
mathematical formulations for volatility, as obtained for the best performing GARCH
type of models in this chapter are obtained as follows.
ECX Options market:
∑∑ = −
=
−− ++=Ω≡p
j jt
q
i
itttt uuE1
2
1
2
1
22 752.0389.00067.0)( σσ (4.17)
In the expression on right hand side of equation (4.17), the second term refers to ARCH
coefficient and the third term corresponds to the GARCH effect. It is clear that GARCH
coefficient 2
jt−σ dominates the model, which means that volatility or uncertainty in the
past determines how volatile or uncertain the markets shall be there in future also.
CCX Futures Market:
2
1
2
11
2
11
22 972.0)(058.400002.00012.0)( −−−− +++=Ω≡ tttttt HuuE σσσ (4.18)
Equation (4.18) is clearly dominated by the non-linear term )( 2
11 −tH σ , which is taken as a
second order quadratic function (Sentana 1995). This means that simple GARCH effect is
totally negligible and complex non-linear terms describe the behavior of voluntary
market of CCX, which makes it quite similar to other financial markets and energy
markets; and different from the compliance market of ECX.
60
4.8 Summary and conclusions
Growing concern over climate change leads to fixing of emission reduction targets in
different countries and regions. To fulfill this requirement, one of the options before the
GHG emitters is to go for carbon trading. As a result, growth in carbon market is
expected to soar (World Bank 2010). As carbon trade grows in importance, so does the
need to model and forecast the price movements in carbon markets. Volatility measures
the average absolute daily change, and is a common approach to indicate the variability
and unpredictability of the price of a tradable commodity. For carbon markets, in
particular, a full understanding of volatility of carbon prices is very critical. Forecasts of
carbon market volatility are important inputs into macroeconomic models and financial
risk assessment calculations like value at risk. Recently, a large volume of literature has
emerged on modeling and forecasting volatility in financial markets and energy markets
like oil and natural gas. In contrast, hardly any work has been done for carbon markets in
this direction. In this chapter, various econometric models are examined for forecasting
market volatility of three major carbon markets; the ECX options market, ECX futures
market and CCX spot market. Major findings of this chapter are explained in this section.
First, time-series data for volatility in all these carbon markets are stationary and there are
no structural breaks in the series despite the policy level transitions in the international
climate change scenario. Due to the stationarity property, volatility can be forecasted for
all carbon markets. An important consequence of this result is that top- level strategic
changes are not affecting the short-run fluctuations and hence market investors need not
be apprehensive about sudden shocks arising out of policy changes in the carbon markets.
Second, for forecasting purposes, GARCH (1, 1) model performs the best for ECX
options market, a finding that is similar to the ECX spot market, which is also forecasted
best by GARCH (1, 1) model (Benz and Trück 2009). This shows the similarity in
volatility behavior of ECX options market and the ECX spot market. On the other hand,
Historical Averages model performs the best for ECX futures market, thereby indicating
that the volatility dynamics of futures market in ECX are different from both spot and
options markets. A possible reason for this difference in volatility of ECX futures market
could be that carbon assets are traded in some future time, for which price is specified at
61
present time (Bodie 2010), which implies different levels of uncertainty and hence
different volatility from ECX spot and options markets. However, one common factor is
that volatility in all the compliance markets of ECX (spot, options and futures) are
described by simple econometric models like GARCH (1, 1) and Historical Averages,
which is quite different from volatility behavior of all other financial markets and energy
markets (spot, options and futures).
Third, non-linear GARCH models perform better than others for the CCX spot market,
thereby indicating different behavior of this voluntary carbon market from the
compliance-bound ECX carbon market. This result is however similar to other financial
markets and energy markets like oil and gas, the volatility of which is also best described
by non-linear GARCH models; thereby indicating the similarity of voluntary carbon
market with conventional markets. High dominance of non-linear component in the
model completely rules out any closeness with simple GARCH models and hence with
the compliance market of ECX.
To sum up, this chapter shows that different carbon markets witness different volatility
patterns and hence separate econometric models are required for forecasting volatility for
each of these markets. The investors in voluntary carbon markets may follow the same
analysis as that of financial markets for predicting uncertainties and calculation of value-
at-risk. However, for the compliance carbon markets, different models have to be used
for forecasting purposes. The difference in compliance markets could possibly arise from
comparison with the marginal abatement costs and transaction costs in compliance
markets.
There are various limitations, however, in this study. First, being one of the pioneering
studies on forecasting carbon markets, it is limited to examination of volatility in price
only. Therefore only univariate models are considered here. Examination of multivariate
models that include trading volume may improve the forecast accuracy. Environmental
variables like weather patterns can further improve the accuracy. Other financial
variables like the number and type of listed companies on the climate exchanges and
policy issues like mandatory fixing of emission reduction targets by the federal or
62
provincial governments in the EU and US may be some other useful variables to be
considered in this effort. Second, different markets became functional at different points
of time and hence slightly different time horizons have been used to forecast volatility.
Accuracy of forecasting might be improved after further passage of time, as more data
become available. Third, the effect of size and liquidity in the carbon market on the
quality of volatility forecasts is also an interesting and yet open question. Fourth, more
trading options have been introduced recently in both ECX and CCX, and their
comparison could bring better results. Finally, no structural breaks were observed in the
volatility of carbon markets, which shows that policy level changes so far did not have
very significant effects on the volatility dynamics of these markets. However, with
significant policy level changes at UNFCCC meets recently, some structural breaks may
arise in the data in future, which will need to be taken into account for further forecasting.
An array of additional financial instruments-options, derivatives, swaps, and so on are
becoming available in different carbon markets around the world to help firms hedge
volatility risk. Further investigation into the use of these models is suggested for all the
new carbon assets when more empirical data from other emerging carbon markets
become available.
Nonetheless, the findings of this chapter may be of immense use at the firm and policy
levels. At firm level, volatility behavior of emission allowances might enable companies
to compare the costs of emissions in their production process with carbon market
uncertainties. It could be useful in deciding not only about spot market investments, but
also about banking and borrowing of the carbon credits for future use. At the policy level,
the study may be helpful in choosing between carbon tax and the market based
instruments. Which of these two key market-based policy instruments, tax or trading,
should have the primary role in practice is much less clear cut. Both are mixed
government-market solutions: with taxes the government sets the carbon price and the
market sets the quantity of emissions; with trading the government sets the quantities of
emissions and the market sets the prices. Neither is, a priori, preferable on such
ideological lines (PWC 2009). Drawing comparisons between the forecasts of various
carbon markets from this chapter with expected returns from a carbon tax, the policy
makers can have a choice to go for either or a mix of the two. Knowledge of volatility
63
behavior in different markets also presents policy makers an ability to choose from
different mechanisms to reduce uncertainties: To allow banking of allowances for future
use for motivating firms to further reduce their emissions now by allowing them to
establish a reserve for the future; or to allow firms to borrow allowances from future
periods; or to set price floor and/or ceiling to reduce the risks to investments in emission
reductions. In general, the results of this study are also going to be useful for anyone from
individual investors to policy makers, whosoever needs to forecast the carbon market
volatility.
64
5 An Agent-Based Model of Carbon Markets
Abstract
Carbon markets comprise of various types of agents such as greenhouse gas emitters,
agriculturists, foresters and individual market investors. Genetically programmed agent
based models, which are the bottom-up simulations of actions, incorporate interactions of
such heterogeneous entities. These models possess considerably higher forecasting
capabilities than the traditional econometric models. Artificial carbon markets obtained
from such agent based models for the spot markets of European Climate Exchange
(ECX) and Chicago Climate Exchange (CCX) have stylized facts – lack of
autocorrelations, volatility clustering, heavy tails, conditional heavy tails, and non-
Gaussianity; which are similar to the actual carbon markets. Experiments are performed
on these artificially simulated carbon markets by changing wealth distribution of agents
from Equal to Pareto, and finally to Maxwell Boltzmann; by varying the distribution of
proportion of carbon assets from Equal to Gaussian; and lastly by changing the number of
agents in the carbon market from 5000 to 100000. Forecast accuracy is further improved
considerably, when the values of these agent parameters are closer to real market
situations. This virtue of experimentation is not available in the world of traditional
econometric models. Hence agent based models could play a key role in mimicking the
real world carbon markets and could provide an alternative to the analytical models.
Key Terms—Carbon market; agent based model; artificial market; genetic programming;
experimentation.
5.1 Introduction
Carbon markets have been recognized as one of most promising ways to stop the increase
of greenhouse gas (GHG) emissions efficiently and effectively (Brohe et.al. 2009). These
markets involve human activities and behavior, as they consist of various heterogeneous
agents such as greenhouse gas emitting companies, transporters, agriculturists, foresters,
individual arbitrageurs, hedgers and market investors. Following Farmer (1998), agents
in carbon market can be divided broadly into two categories: fundamental traders and
65
technical traders. Fundamental traders take decisions on trading of a carbon asset if the
price of that asset departs from a value that they perceive as the fundamental one
(Martinez-Jaramillo and Tsang 2009). The price dynamics for such traders are driven up
and down by various factors like their marginal abatement costs (MAC); the ambition of
firms to increase their production capacity; to fulfill emission reduction targets
requirements fixed by the regulator in compliance markets; and to achieve the goal of
corporate social responsibility in voluntary markets. On the other hand, technical traders
make their investment decision rules purely on the basis of the market price of carbon
(Brock et.al. 1992). Technical analysis is an important tool for investment decision-
making and is being used extensively in other financial markets also (for example,
Dempster et.al., 2000, Raberto et. al., 2008, Alfi et.al., 2009, and Martinez-Jaramillo and
Tsang, 2009). Specifically for carbon markets, the World Bank report on state and trends
of carbon market (Kossoy and Ambrosi 2010) also argues that the trading in world’s
carbon markets so far is predominantly technical in nature. Therefore, for the purpose of
this chapter, it is presumed that agents in carbon market are technical traders, who make
investment in carbon markets purely on the basis of price movements in the market.
Due to heterogeneity among agents that comes from several sources: age, amount of cash
and carbon assets, total wealth, information, time horizon, and desired rate of return;
carbon markets have time-series for price and volume fluctuations, which provide some
of the big puzzles to be solved by the agents (Winker and Gilli 2001). Standard
econometric models like those used in financial markets (for example, Bollerslev, 1986;
Akgiray, 1989; Pagan and Schwert, 1990; Brailsford and Faff, 1996; Yu, 2002; Brooks
and Persand, 2002, 2003) and also in carbon markets (for example, Seifert et.al. 2008;
Homberg and Wagner 2007 and Chapter 3 and 4 of this thesis) for solving these puzzles
are based on fully rational behavior of homogenous agents. However, despite
overwhelming empirical support for the standard models, they cannot adequately
describe all typical features of market time series. Empirical features as volatility
persistence, excess kurtosis, equity premium, large Sharpe ratios, and predictable
deviations from fundamentals still do not have generally accepted explanations (LeBaron,
Arthur, and Palmer 1998), which might be due to heterogeneity of agents, because of
which it is difficult to expect completely rational behavior (Chen and Yeh 2002). To
66
allow for limited rational behavior of the agents, it would be appropriate to explore the
world of agent based models (like for example, Martinez-Jaramillo and Tsang 2009;
Tesfatsion, L. 2005; Tseng 2010), where interactions between agents are taken explicitly
into account that influence the outcomes of market price. An agent-based model is a
bottom-up simulation of the actions and interactions of multiple autonomous entities for
the purpose of analyzing the emergent effects on a system as a whole (Witkam 2010).
Agent based models have already been applied to financial markets, for example, by
using the methodologies of non-equilibrium statistical mechanics to elucidate the
mechanisms underlying the complexity by Mantegna and Stanley (2000); using critical
phenomenon by Stanley et.al. (2002); and using self-organized criticality by Scheinkman
and Woodford (1994). Most influential work in this direction, however, is carried out by
Santa Fe Artificial Stock Market (Arthur et.al., 1997) and Artificial Economic Life
(Palmer et.al., 1994). A good discussion of computational finance is also given in Tsang
and Martinez-Jaramillo (2004); of agent based financial markets in LeBaron (2001); and
of agent based computational economics in Tesfatsion (2001). Complexity of the agent
behavior is the main motivation for using alternative methodologies to gain a better
understanding of some of the unsolved problems in carbon market dynamics. Agent-
based models have shown to be able to simulate complex systems better than traditional
mathematical finance. The model consists of a population of agents, representing
investors with their own assets and trading strategy and a price discovery mechanism that
represents a market (LeBaron, Arthur, and Palmer 1998).
Prices in carbon market are established by investors with different decision making
methods and different investment goals such as risk preference and time horizon.
Complex dynamics of these heterogeneous investors and the resulting price formation
process require a simulation model of multiple heterogeneous agents and a virtual market
or an agent based market. Complex behavior as seen in actual markets can emerge from
simulations of agents with relatively simple decision rules (Witkam 2010) in such
markets. These artificial markets are inspired by the notion that markets can be seen as an
adaptive, complex system with rich dynamics and emergent properties. Such properties
should arise endogenously rather than being imposed exogenously. By using this
approach the intention is to overcome the limitations of traditional theory in which many
67
unrealistic assumptions have to be made to allow tractability (Tseng et.al 2010). Research
in this field is increasingly gaining acceptance in the fields of ecology, environment and
economics (Mzuta and Yamagata 2005). Different studies in this field differ from each
other in the set of assumptions made, and the methodology and tools used; but the
evolved markets share the same common property: the macro behavior of such market,
depicted by the price movements, should emerge endogenously as a result of the micro-
interactions of the heterogeneous market participants. This chapter, therefore, is focused
on study of an agent based model for traders who invest in carbon assets depending on
price movements in the carbon market. The main objective is to model the artificial
carbon market by use of a simple market mechanism and computationally sophisticated
genetically programd agents. The resemblance of this artificial market to the real market
is checked through verification of stylized facts of both. In addition, experiments are
conducted on such an artificial market to understand the carbon market behavior in
response to changes in circumstances. Such behavioral dynamics are studied by varying
different parameters in the artificial market and observing the change in price
movements.
The rest of this chapter is organized as follows. Section 5.2 describes the theoretical
framework for the model of agents and the model of price determination apart from
trading rules of agents. Section 5.3 provides the details of Adaptive Modeler, the software
platform for carrying out agent based modeling. Section 5.4 explains the parameters of
the agent based model. In Section 5.5 the statistical properties or the stylized facts of
carbon markets are explained. In Section 5.6, artificial carbon markets are simulated and
their stylized facts are compared with the real world markets. In section 5.7, experiments
to be performed on artificial carbon market are explained. Section 5.8 describes the
results of these experiments. Section 5.9 presents summary and conclusions.
5.2 Theoretical Framework
In this chapter, the basic framework of Santa Fe Institute (SFI) and that of the standard
asset pricing model of Grossman and Stiglitz (1980) is followed for developing an
artificial carbon market, which is a simulated market created on a software platform using
an agent-based model. This artificial market allows a user to experiment with different
68
scenarios using various combinations of traders, behavior and characteristics. Carbon
markets are populated by heterogeneous traders that interact with each other by means of
buying and selling of the carbon assets, which are emission allowances that are allotted to
them by means of allotment or auction by the government in the compliance market; or
purchased from voluntary market as a matter of corporate social responsibility (Benz and
Trück 2009). The goal of each of the agents is to maximize the expected utility based on
the forecast of the future price of carbon assets. In this section, the abstract model and its
main characteristics are explained.
5.2.1 Model of agents
The agent part includes the objectives of carbon market agents and their utility functions.
For simplicity, it is assumed that all agents in carbon market have same utility function,
which is a constant absolute risk version (CARA) utility function:
)exp()( ,, titi WWU λ−−= (5.1)
where Wi,t is the wealth of agent i at time-period t, and λ is the degree of relative risk
aversion. Agents can accumulate wealth or step up their industrial production process by
purchasing carbon instruments or bank carbon assets for future use by making
investments in the carbon market. By following the approach of SFI, it is assumed that
there are two assets available to an agent in the carbon market. One is the riskless
interest-bearing asset called money, denoted by Mi,t, and the other is a risky asset, the
carbon instrument, denoted by ci,t. At each point in time, each agent has these two options
to keep his wealth, which can be written mathematically as
tittiti cPMW ,,, += (5.2)
Given this combination of money and carbon assets (Mi,t , ci,t), an agent’s total wealth
Wi,t+1 , during next period of time t+1 is therefore,
)()1( 11,,1, +++ +++= tttititi dPcMrW (5.3)
69
Pt is the price of carbon asset at time period t; r is the risk-free interest rate; and dt is per
asset stochastic dividend obtained by the market traders in terms of benefits arising out of
increased production levels, reduction in abatement costs or using these assets at some
future time. Following (LaBaron 2002), it is assumed that dt follows the following mean-
reverting autoregressive Ornstein-Uhlenbeck process:
ttt dddd µρ +−+=−
−
−
)( 1 (5.4)
where −
d is the mean dividend, ρ is the speed of mean reversion, and tµ refers to
stochastic shocks which are normally distributed with mean zero and variance 2
µσ . The
price of carbon asset, Pt, is determined endogenously in the market. Given that the wealth
is dynamic, the goal of each agent is to maximize the expected utility function over one
period,
))exp(())(( ,1,1,, ttititi IWEWUE ++ −−= λ , subject to equation (5.3), where (.),tiE is agent i’s
conditional expectations of 1+tW given his information set tiI , . The choice variable of this
optimization problem is tic , , the number of carbon assets at time t. Under the assumption
of normally distributed market returns, the amount of carbon assets tic ,ˆ that agents desire
to hold is determined as
2
,
11,
,
)1(][ˆ
dPt
tttti
ti
rPdPEc
+
++ +−+=
λσ, (5.5)
where ][ 11, ++ + ttti dPE is I’s expectation in t about next period’s realization of the carbon
asset price and dividend, and 2
, dPt +σ the empirically observed variance of the asset’s
combined price plus dividend time series (LaBaron 2002).
5.2.2 Model of price determination
Demand for carbon assets by an agent is the difference of his actual and desired asset
holdings. Once agents have determined their effective demands, they submit them to a
70
market specialist, who tries to balance the effective demands by setting a market clearing
price. Given tic ,ˆ , the market mechanism is described as follows. Let tib , be the bids or
number of carbon assets that agent i would like to buy at period t, and let tis , be the offers
or number of assets that agent i would like to sell at period t. It is clear that
1,,,ˆ
−−= tititi ccb , if 1,,ˆ
−≥ titi cc
0, otherwise (5.6)
and
tititi ccs ,1,,ˆ−= − , if 1,,
ˆ−≤ titi cc
0, otherwise (5.7)
It is apparent from equations 5.6 and 5.7 that an agent can only buy or sell but not both at
the same time. Furthermore, let
∑=
=N
i
tit bB1
, (5.8)
and
∑=
=N
i
tit sS1
, (5.9)
be the totals of bid and offers, respectively for carbon asset at time t, where N is the
number of agents. Following Palmer et. al. (1994), there is a very simple price adjustment
scheme, based solely on excess demand Bt-St:
))(1(1 tttt SBPP −+=+ β (5.10)
Where β is a function of the difference between Bt and St. β can be interpreted as the
speed of adjustment of prices that follows the hyperbolic tangent function.
71
5.2.3 Trading rules and expectation formations
Agents make use of trading rules to make predictions on the mean and variance of returns
in carbon market. A rule tells each agent how to forecast future returns, and what the
conditional variance of this forecast is. While traders are homogeneous with respect to
their utility functions and degrees of risk aversion, they differ when deriving their
expectations ][ 11, ++ + ttti dPE . Price forecast is generated by using individual trading rules
of the type
If (condition fulfilled), then (derive forecast)
First, a forecast is produced using equation (5.5), and then will be converted into an
action, i.e., an agent’s bid or offer for carbon asset. Each of the j trading rules that every
agent possesses consists of a condition part, a forecast part (predictor), a fitness
parameter and forecast accuracy i.e.
rulei,j = (condition part); (predictor); fitness parameter, forecast accuracy
The condition parts, as defined by equations (5.6) and (5.8) are checked against a
Boolean market descriptor, which holds current and past information on price. From the
set of j individual trading rules, normally several rules match the market descriptor.
Agents chose one of them for forecast production, selecting the best rule, based on
forecast accuracy (LeBaron 1999). Finally, the agent determines the forecast, assuming it
to be linear in current price and dividend.
jtjjttti bdPadPE ++=+ ++ )()( 11, (5.11)
The subscript j refers to the rule chosen by agent i. This restricted forecasting rule along
with the demand for carbon assets gives a demand function which is linear in Pt. Setting
the total number of carbon assets to a fixed value allows for solution of the demand
equation (5.5) for a temporary equilibrium price. This assumption is justified as total
number of assets is fixed by the regulator depending on the overall cap on emissions.
After the price is set, agents update their portfolios, and trading volume is recorded.
72
5.2.4 Learning
For the purpose of forecasting prices in artificial carbon markets, an individual is viewed
or modeled as a collection of decision rules, which dictate the actions to be taken in given
situations and a set of preferences used to evaluate the outcomes arising from particular
situation-action combinations. These decision rules are continuously subject to review
and revision; new decision rules are tried and tested against experience, and rules that
produce desirable outcomes supplant those that do not (Lucas 1986). For modeling of this
learning process, the technique of genetic programming is used, in which agents are
represented by computer programs. This technique has been used in the past to perform
technical analysis by various research groups like Garcia-Almanza and Tsang (2006),
Markose et.al (2003), Dempster et.al. (2001), Yeh and Chen (2000), Edmonds (1999),
Edmonds and Moss (1997), Neely et.al. (1997); and has been described as a suitable way
to model economic learning in Brenner (2005). Genetic programming (GP) is an
evolutionary computing technique inspired by biological evolution to optimize a
population of agents or the computer programs to perform a certain task. Computer
programs are created from a high level problem statement and are the lingua franca for
expressing solutions to a wide variety of problems. The first generation of agents or
programs is created randomly. GP then breeds a population of computer programs
genetically using the principles of Darwinian Natural Selection and biologically inspired
operations like reproduction, mutation and cross-over (Koza 1992). These programs are
evaluated by a fitness function that measures how well the program performs the task or
solves the problem. Fitter programs get selected over less fit programs to participate in
reproduction or recombination operations to create a new generation of programs or
agents. In a recombination operation such as crossover, randomly chosen parts (sets of
genes) of two programs are exchanged to create two new programs. A mutation operator
can also be applied to randomly change a small part of a program (Witkam 2010, 34-36).
The process of creating new generations is repeated until one or more agents or programs
in the population have achieved a satisfactory fitness level. A typical flowchart of
Genetic Programming is given in Koza (1992) and is reproduced in Appendix-1.
73
5.3 Adaptive Modeler- The Software Platform
To develop an artificial carbon market in this chapter, a GP-based software system called
Adaptive Modeler is used, which constitutes basic platform for the design of investment
strategy of agents. Important features of this software are described in this section.
Adaptive Modeler consists of an agent-based model that receives price quotes from the
real world carbon markets and produces price forecasts. This framework is depicted in
Fig. 5.1. The model consists primarily of a population of agents and a virtual carbon
market (VCM), where agents can trade the security. An agent is an autonomous entity
representing a trader or investor with its own assets, which could be cash and/or carbon
instruments and its own trading strategy. After initialization, a new model starts evolving
by executing its regular cycle for every received quote price on daily basis from the
carbon market.
Fig. 5.1. Cycle of an agent based model in Adaptive Modeler
After a new price quote bar from carbon market is received every day, agents can place a
new order or remain inactive according to their trading strategy, which is buying or
selling according to equations (5.8) or (5.9). After all agents have evaluated their trading
Agent-based
Model Cycle
Receive new price quote daily from real-world carbon market
Breeding Agents evaluate trading rules and place orders
Virtual market clearing and forecast
74
strategy, the virtual carbon market determines the clearing price using equation (5.10),
executes all executable orders and releases the price forecast for the next day. Finally,
breeding of new agents and replacement can take place by evolutionary operations such
as crossover and mutation. Total amount of wealth in the model keeps varying because of
agent replacements due to evolutionary operations. Total number of carbon assets that
exist in the model also changes because of agent replacements. This process then repeats
itself for the next quote price received on next day (Witkam 2010).
5.4 Model Parameters
In Adaptive Modeler, a model initialization is done for a population of agents according
to specified parameters. The parameters of the model used in this chapter are described in
this section.
5.4.1 Population Size
Population size is the total number of agents in the model of carbon market. Bigger the
population, more are the trading rules competing and evolving in parallel. This increases
the chance of new trading rules with rise of new opportunities in the market. A bigger
population also increases the ability of a model to endure different market regimes as
more strategies could be stored in the trading rules of agents. A larger population size
also increases model stability and prevents models from extreme forecasts or from a state
of imbalance (Koza 1992). However, bigger populations require more computations and
make model evolution slower.
5.4.2 Wealth distribution
Wealth distribution is an important parameter of agents and has a great influence on the
artificial or virtual market price. If initial wealth is assigned to agents by making use of
random sampling methods, noise might be added to the price discovery mechanism
(Witkam 2010). To avoid such noise, equal initial wealth is generally assigned to all
agents. However, it is not expected to be close to reality as agents with different wealth
are trading in the actual carbon market.
75
5.4.3 Position distribution
Position distribution is the proportion of carbon allowances to the total wealth of an agent
and another important parameter in an agent based model. It is fixed initially and then-
after it keeps varying during model evolution because of agent replacement. Furthermore,
initial position of an agent gets changed immediately after its creation as a consequence
of trading according to its trading rule. The position distribution may therefore diverge
from the chosen initial distribution during model evolution.
5.4.4 Basis of forecast
In Adaptive Modeler, one can specify whether the forecast should be based on i). Virtual
Market Price (VMP), which is the clearing price on the Virtual Market, based on the
orders that are placed by all the agents; or on ii). Best Agents Price (BAP), which is the
price, calculated using only the orders of a group of best performing agents. The size of
the Best Agents group can be specified as a percentage of the total population size, which
is fixed at 2.5% for experiments in this chapter. The rationale for using the virtual market
price as an indicator for future prices that due to the volume weighted clearing price
computation mechanism, wealthier or more successful agents, who generally place bigger
orders, will have a bigger influence on the market price than less wealthy or less
successful agents. This way the forecast calculation mechanism has a preference for
successful trading strategies but still includes a high number of diverse trading strategies.
Hence VMP is needed to make the forecasting mechanism more robust to changes in
market behavior since previously successful trading strategies are not guaranteed to
remain successful in the future (Witkam 2010). However, it is interesting to compare the
forecasting abilities of the entire Virtual Market with those of a much smaller group of
only the best performing agents.
5.4.5 Trading rules
Each agent receives a technical trading rule, called genome that is randomly created
according to the genome settings in genetic programming. After all initialization
processes, the agent population evaluates its trading rules, and then trade, and finally
breed, according to the agent-based model cycle. Trading rules in Adaptive Modeler use
76
carbon market price data as input and, according to their internal logic, return an advice
consisting of a desired position of carbon assets, as a percentage of wealth.
5.4.6 Breeding
Breeding is the process of creating new agents to replace poor performing agents and is
implemented with Genetic Programming (GP) technology. Breeding occurs by selecting
pairs of well performing agents (parents) and producing new genomes by recombination
of the parent genomes through a crossover operation. In a crossover operation, the parent
genomes are copied and then a randomly chosen part of the copied genome of one parent
gets exchanged for a randomly chosen part of the copied genome of the other parent
(Koza 1992). The resulting two new genomes are used to create two new agents. In
Adaptive Modeler a steady-state approach for generations is used in which only a small
part of the population is replaced at a time, typically every day, instead of the entire
population at once. This allows for a gradually changing population which is necessary to
maintain a certain degree of model stability. Parents are selected according to the
parameters minimum breeding age, which is fixed at 80 days in this study. First an initial
selection is made. This is a temporary sub population in which breeding and replacement
takes place. The initial selection consists of a given percentage of all agents of minimum
breeding age and older. Thenafter p best performing agents are selected as parents,
judged by the breeding fitness return of the initial selection, where p is the value of parent
selection parameter (Witkam 2010). In this chapter, p is kept fixed at 2.5%.
5.5 Statistical Properties of Carbon Markets
In this chapter, price time-series data from two carbon markets is taken: European
Climate Exchange (ECX) spot market, which is a compliance market and Chicago
Climate Exchange (CCX) spot market, which is a voluntary carbon market. For the sake
of brevity, ECX and CCX shall be used to indicate these two spot carbon markets,
respectively, throughout the chapter. Following (Yu 2002), statistical analysis is
performed on these time-series using log returns, which are defined in the following way:
1
1
log −
−
−=≡ tt
t
tt pp
P
Pr (5.12)
77
where tt Pp log≡ . The advantage of using this type of return is that it is easier to derive
the time-series properties of an additive process than multiplicative processes. Fig. 5.2
illustrates the daily closing prices and Fig. 5.3 depicts log returns for ECX. Similarly Fig.
5.4 and Fig. 5.5 indicate the same statistics for CCX.
Time-series of log returns in financial markets exhibit some interesting statistical features
known as stylized facts, which are a very important benchmark for the research in
artificial markets (Martinez-Jaramillo and Tsang 2010). In financial markets, they are
seen as the first verification criteria for building a simulated market. Many different types
of stylized facts are found in the already existing market literature. However, for the two
markets, the approach of Winker and Gilli (2001) is followed and five stylized facts are
considered, which the most common ones are; and different tests are performed to verify
that our endogenously generated price in the model mimics these statistical properties.
10
20
30
40
50
Price
0 200 400 600 800 1000Time (Days)
-.1
0.1
.2Log Return
0 200 400 600 800 1000Time (Days)
Fig. 5.2. Closing Prices ECX Fig 5.3. Log Returns ECX
78
02
46
8Price (US$)
0 500 1000 1500 2000Time (Days)
-.4
-.2
0.2
.4Log Return
0 500 1000 1500 2000Time (Days)
Fig. 5.4. Closing Prices CCX Fig 5.5. Log Returns CCX
5.5.1 Lack of autocorrelations
Autocorrelation is the cross-correlation of a time-series with itself. It is the similarity
between observations as a function of the time separation between them and is a
mathematical tool for finding repeating patterns. Linear autocorrelations of log returns
are generally insignificant for financial time-series (Winker and Gilli 2001). Since the
data consists of daily time-series for the two carbon markets, so testing is carried out for
the same. The autocorrelation function is defined as
C (τ) = corr (rt, rt+ τ) (5.13)
where τ is the time lag.
From Fig. 5.5 and Fig. 5.6, it is observed that the autocorrelation of the log returns for
different time lags fluctuates around zero for ECX and CCX. So this property is satisfied
for both real world carbon markets.
79
-0.40
-0.30
-0.20
-0.10
0.00
0.10
AC logreturns ECX
0 10 20 30 40Lag
-0.10
-0.05
0.00
0.05
0.10
AC logreturn CCX
0 20 40 60 80 100Lag
Fig 5.6. Autocorrelations log returns ECX Fig 5.7. Autocorrelations log returns CCX
5.5.2 Volatility clustering
Different measures of volatility display a positive autocorrelation over several days,
which indicate that high-volatility events tend to cluster in time (Martinez-Jaramillo and
Tsang 2010). The autocorrelations of absolute log returns allow investigating this
phenomenon. Empirical studies, for example by Manderbolt (1963) have shown that the
autocorrelation function of absolute returns remains mostly positive and decays over
several lags. This is interpreted as a sign of long range dependence. For both of real-
world carbon markets, this property also holds true, as is evident from Fig. 5.8 for ECX
and Fig. 5.9 for CCX.
5.5.3 Heavy tails
In probability theory, heavy-tailed distributions are probability distributions whose tails
are not exponentially bounded, that is, they have heavier tails than the exponential or the
normal distribution.In order to be able to determine the tail distribution, the log returns’
kurtosis is reported, which is the fourth central moment of a distribution and it measures
the degree of flatness of a distribution near its center (Lux 1998). Distribution of daily
and higher frequency returns in financial markets displays a heavy tail with positive
excess kurtosis. For a normal distribution, the kurtosis is three. If it is more than three, the
phenomenon is known as excess kurtosis and is an indication of fat tails (Wooldridge
2008).
80
-0.20
0.00
0.20
0.40
AC absolute logreturns ECX
0 10 20 30 40Lag
-0.05
0.00
0.05
0.10
0.15
0.20
AC absolute logreturn CCX
0 20 40 60 80 100Lag
Fig 5.8. Autocorrelations absolute log returns ECX
Fig 5.9. Autocorrelations absolute log returns CCX
It could be observed from Table 5.1 that Kurtosis for the log returns of ECX and CCX
follow a fat tail distribution and hence satisfy this property.
Table 5.1. Statistics for log returns for price in ECX and CCX
Statistics Log-Return
ECX CCX
Kurtosis 221 328
J-B Test H 1 1
ARCH 0.235 0.141
GARCH 0.176 0.310
5.5.4 Conditional heavy tails
Even after correcting returns for volatility clustering (e.g. via GARCH-type models), the
residual time series still exhibit heavy tails. However, the tails are less heavy than in the
unconditional distribution of returns. This property is tested by checking the values of
ARCH and GARCH coefficients. If both the coefficients are less than one, the property
of conditional heavy tails is satisfied (Martinez-Jaramillo and Tsang 2010). From Table
5.1, it is clear that this property is satisfied by both the carbon markets.
81
5.5.5 Non-Gaussianity
Market returns fail to be normally distributed, as financial series, particularly logarithmic
returns, are believed to be non-normal, partly due to the fat tails. Following Lux (1998),
this property is checked using Jarque-Bera test. For both ECX and CCX carbon markets,
the test values reject the null hypothesis that the sampled data is drawn from a normal
distribution. Hence the time series data in both the carbon markets satisfy non-gaussianity
property also.
Therefore the real market data from both the carbon markets of ECX and CCX satisfies
all the stylized facts of financial markets and hence simulation could be carried out for
these markets, which is done in subsequent sections.
5.6 The Simulation
For simulating artificial carbon markets in Adaptive Modeler, it is assumed that both the
carbon markets of ECX and CCX operate as if each trading round is one day. The results
of simulation runs for agent based model on the data from European Climate Exchange
(ECX), and the Chicago Climate Exchange (CCX), are presented in this section. The
statistics for the actual and artificially simulated carbon markets are shown in Table 5.2.
Table 5.2. Summary Statistics for the Log Returns of prices of actual and
artificially simulated carbon markets
Actual Carbon Markets Artificial Carbon Markets
ECX CCX ECXA CCXA
Mean -0.0031 -0.0023 -0.0027 -0.0018
Max 0.881 3.26 0.732 3.91
Min -1.27 -3.04 -1.85 -3.69
Skewness -5.40 0.54 -7.74 0.43
s.d. 0.62 0.19 0.57 0.21
Variance 0.0072 0.037 0.0086 0.050
82
Tests are conducted for the statistical properties or the stylized facts on the time-series of
log returns for the two simulated markets using both Virtual Market Price (VMP) and the
Best Agents Price (BAP). It is verified whether the simulated prices in the model mimic
the statistical properties of real-world carbon markets or not. The findings are described
subsequently.
5.6.1 Lack of autocorrelations
Linear autocorrelations of log returns are found to be insignificant for both the simulated
markets for both virtual market price (Fig. 5.10 and Fig.5.12) and the best agents’ price
(Fig. 5.14 and Fig. 5.16). It can be easily observed that the autocorrelation of the log
returns for different time lags is around zero for both ECX and CCX under both the
options of VMP and BAP. Hence the simulated artificial carbon markets follow stylized
fact for lack of autocorrelations.
.
-0.30
-0.20
-0.10
0.00
0.10
AC logreturns ECX VMP
0 10 20 30 40Lag
-0.10
0.00
0.10
0.20
0.30
AC absolute logreturn ECX VMP
0 10 20 30 40Lag
Fig 5.10. Autocorrelations log returns ECX,
VMP
Fig 5.11. Autocorrelations absolute log returns
ECX, VMP
83
-0.20
-0.10
0.00
0.10
AC logreturn CCX VMP
0 20 40 60 80 100Lag
-0.05
0.00
0.05
0.10
0.15
0.20
AC absolute logreturn CCX VMP
0 20 40 60 80 100Lag
Fig 5.12. Autocorrelations log returns CCX,
VMP
Fig 5.13. Autocorrelations absolute log returns
CCX, VMP
5.6.2 Volatility clustering
Figures 5.11 and 5.13 show that for both simulated carbon market under VMP, the
autocorrelation function of absolute returns remains positive and decays over several
lags. So the stylized fact of volatility clustering is also satisfied by both the simulated
carbon markets under VMP. However, this fact is not satisfied for BAP, as is evident
from Fig. 5.15 and 5.17 for the simulated markets of ECX and CCX, respectively
-0.05
0.00
0.05
0.10
AC logreturns ECX BAP
0 10 20 30 40Lag
-0.05
0.00
0.05
0.10
AC absolute logreturns ECX BAP
0 10 20 30 40Lag
Fig 5.14. Autocorrelations log returns
ECX, BAP
Fig 5.15. Autocorrelations absolute log
returns ECX, BAP
84
-0.30
-0.20
-0.10
0.00
0.10
0.20
AC logreturn CCX BAP
0 20 40 60 80 100Lag
-0.10
0.00
0.10
0.20
0.30
AC absolute logreturn CCX BAP
0 20 40 60 80 100Lag
Fig 5.16. Autocorrelations log returns
CCX, BAP
Fig 5.17. Autocorrelations absolute log
returns CCX, BAP
5.6.3 Heavy tails
The distribution of daily and higher frequency returns is also checked for the simulated
markets for positive excess kurtosis. From Table 5.3, it is clear from the values of
kurtosis that log returns for both simulated markets follow a fat tail distribution under
both VMP and BAP criteria. Hence the price series of simulated markets satisfy this
statistical property also.
Table 5.3. Statistics for the log returns for the price series of the
simulated carbon markets of ECX and CCX
Virtual Market Price Best Agents Price
ECX CCX ECX CCX
Kurtosis 221 328 497 489
J-B Test,
H -value
1 1 1 1
ARCH 0.533 0.387 No results No results
GARCH 0.708 0.881 No results No results
85
5.6.4 Conditional heavy tails
From Table 5.3, it is evident that both ARCH and GARCH coefficients are less than one
for VMP, thereby indicating that this stylized fact is satisfied by the artificially simulated
carbon markets under virtual market price criterion. However, under BAP criterion, no
values are returned for both the markets, again indicating failure of the model under best
agents’ price criterion.
5.6.5 Non-Gaussianity
This statistical property is checked using Jarque-Bera test on price-series of both
simulated markets. From Table 5.3, it is evident that for the price-series both the
simulated markets for ECX and CCX, the test values reject the null hypothesis that the
simulated data follows a normal distribution. Hence the time series data in both the
artificial carbon markets satisfy non-gaussianity property also under both VMP and BAP
criteria.
From this section, it is evident that the simulated carbon markets using an agent-based
model satisfy the statistical properties or the stylized facts of the financial markets under
virtual market price criterion and hence could be used for forecasting purposes. However,
all stylized facts are not satisfied for the best agents’ price. Even for the virtual market
price, it would be important to adjust parameters of the model, so as to achieve maximum
accuracy of forecast. Next section is devoted to carrying some experiments with the two
artificial markets to improve forecast capabilities of the agent-based model in carbon
markets.
5.7 Experimentation with artificial carbon markets
This section describes a series of experiments performed on the artificial carbon markets
of ECX and CCX using Adaptive Modeler software with an aim to understand carbon
market behavior. Three experiments are performed to see how forecasting performance
changes in the artificial markets, when model parameters are changed. Three sets of
parameters involved in the simulation are: wealth distribution; proportion of allowances;
and the number of agents. Other parameters are kept fixed for the sake of simplicity. For
86
analytical econometric models, Brooks (1998), Yu (2002), Bollerslev (1986), Akgiray
(1989), Pagan and Schwert (1990), Benz and Trück (2009) and Chapter 4 of this thesis
indicate that in financial markets and carbon markets, most of the price series are
described most accurately by GARCH types of models. In this section, a comparison is
also made for forecasting performance of GARCH type of models with agent based
models. The rationale for using these parameters for experimentation is explained first.
5.7.1 Wealth distribution of agents (W)
In both the carbon markets of Europe and Chicago, there is an involvement of agents of
diverse backgrounds. In Europe, emission reduction targets are fixed by the regulator,
whereas in Chicago, the involvement of agents is purely on voluntary basis. Even though
the nature of EU and Chicago market is different in this respect, there is one common
factor: agents with different wealth levels are participating in both of them. Therefore it
appears reasonable to see how forecasting performance of the model changes when we
change the wealth distribution of the agents in the artificially simulated markets. For
experimentation in this chapter, initial wealth is assigned to the agents by the following
methods:
(a). Equal for all agents: All agents are assigned the same initial wealth. Though it is not
realistic to expect equal wealth for all agents in the real market, it could be a good
starting point for simulation exercise.
(b). Pareto distribution: Here, the agent wealth is randomly sampled from a Pareto
distribution, which is a well known power law distribution commonly used to describe
wealth or income distributions. In particular it describes an unequal distribution where a
large part of total wealth is owned by a small percentage of individuals, generally in the
80-20 ratio. Pareto distribution has been used considerably in the financial market
literature, for example by Reed (2010) to describe wealth of a population of agents; and
hence is used in experimentation for the purpose of this study also.
(c). Maxwell-Boltzmann distribution: Agent wealth can also be randomly sampled from a
Maxwell-Boltzmann distribution. This is an exponential distribution originating from the
87
field of statistical mechanics for describing the distribution of energy of atoms in a gas. In
econo-physics, for example, by Mantegna and Stanley (2000), its general significance has
been recognized for describing the distribution of money among agents in an economy.
Although money may be considered conserved in a closed economy, wealth, when it
includes non-cash assets, is not necessarily conserved. Wealth may change due to
changes in asset prices or through the creation and destruction of assets. For example, in
carbon markets, agents may keep selling, buying or retiring carbon credits, depending
upon their emission reduction commitments, production enhancement motives or social
and environmental obligations. Maxwell-Boltzmann distribution is the most random
distribution among all of these distributions (Laurendeau 2003).
5.7.2 Proportion of carbon allowances vis-à-vis total wealth (P)
In EU countries, due to fixing of targets under Kyoto Protocol, CO2 allowance
distribution is done by the government to different emitters. The allowances are either
allotted or auctioned initially by the government regulator within the overall cap on
emissions. Subsequently, if any company wishes to emit more, it has to buy allowances
from the market. Similarly those companies that have reduced their targets below the
fixed levels can sell the surplus allowances. However in USA, there is no government
regulation for the emission targets. So it is completely up to the emitters to buy or sell
carbon allowances in the market (Point Carbon 2009). This makes the nature of EU and
Chicago markets different from each other. Therefore it is expected for the model to
perform in a different way for changing the proportion of carbon assets among different
agents. Therefore an experiment is performed to compare the forecasting accuracy of the
agent based model by varying initial proportion of carbon assets in these markets by two
distributions: (a). Equal: When all agents get the same initial allotment of carbon assets.
The position can be specified initially and is chosen to vary within [-100%, 100%]; and
(b). Gaussian: Where an agent’s position is randomly sampled from a Gaussian (Normal)
distribution with the specified mean and standard deviation. The mean is chosen to vary
within [-100%, 100%].
88
5.7.3 Number of agents (N)
Carbon markets are expanding day by day. With more and more countries fixing
emission reduction targets and the growing environmental consciousness, it is expected
that more carbon markets will be established around the world. Already the markets have
become operational in China, Japan, Australia and various other countries (World Bank,
2009). As a result, it is expected that the number of agents will also go on increasing in
the times to come. Therefore it seems reasonable to carry out experiments to see the
forecasting performance of an agent based model with change in the number of agents N.
This experiment is performed with N equal to 5000, 25000, 50000 and 100000 and
change in forecasting accuracy is noticed.
Following Yu (2002), comparison of artificially simulated markets with real carbon
markets is made using the two evaluation measures of Root Mean Square Error (RMSE)
and Mean Absolute Error (MAE) to see the forecasting accuracy. These evaluation
measures are defined as
RMSE = ∑=
−I
i
ii ppI 1
2)ˆ(1
(5.13)
MAE = ∑=
−I
i
ii ppI 1
ˆ1
(5.14)
Where, ip is the forecasted price, ip is the carbon price from actual data on ith day and I
the number of days of trading.
5.8 Results and discussion of Experiments
The results of experiments show very striking findings in the use of agent based models
for forecasting in carbon markets. One common finding in these experiments is that both
the indicators perform consistently for the two markets and for different parameters, as
shall be clear from the subsequent discussion.
89
5.8.1 Changing W
The results of experiments, by changing wealth of agents, performed on the simulated
markets of European Climate Exchange (ECX) and the Chicago Climate Exchange
(CCX) are given in Table 5.4. From these results, it is evident that forecasting accuracy
using both the performance indicators improve continuously as the initial distribution of
wealth is changed from Equal to Pareto and then to Maxwell-Boltzmann for both ECX
and CCX. The numbers in parenthesis indicate the rank in forecasting accuracy.
Table 5.4. Results of experiments on artificial carbon markets for different wealth
distribution of agents
ECX CCX
Initial wealth distribution
Equal Pareto Maxwell-Boltzmann
Equal Pareto Maxwell-Boltzmann
RMSE 0.092
(3)
0.057
(2)
0.013
(1)
0.086
(3)
0.065
(2)
0.032
(1)
MAE 0.075
(3)
0.026
(2)
0.003
(1)
0.067
(3)
0.035
(2)
0.015
(1)
Figures in parentheses indicate ranking of forecasting accuracy
The results obtained in Table 5.4 indicate that for forecasting both compliance and
voluntary carbon markets, maximum accuracy of forecast is obtained, when we allot
initial wealth among agents according to Maxwell-Boltzmann distribution. This result
seems quite intuitive, as investment agents in both types of carbon markets are expected
to possess any amount of wealth, which is also a reflection of the size of their respective
firms. Taking wealth distribution as equal or Pareto introduces forecasting error, as
behavior of real market agents is not followed completely by the artificial agents in the
learning process or formation of trading rules.
90
5.8.2 Changing P
The results of experiments by changing proportion of carbon assets of agents, performed
on the simulated markets, are given in Table 5.5. The numbers in parenthesis indicate the
rank in forecasting accuracy. From these results, it can be observed that both the
evaluation measures show better forecasting accuracy by the model when we consider
equal distribution for proportion of allowances for the compliance market of ECX.
However for the voluntary market of CCX, the performance using both the measures is
better for Gaussian distribution. In compliance markets, all the agents get equally
proportioned allotment of allowances by the regulator, depending upon their level of
emissions in the beginning of commitment period. So by taking equal distribution in
model, the performance is expected to be better, which is true in this case. However, in
Chicago market, there is no allotment of allowances by the regulator and the companies,
investors or the agents are trading purely on voluntarily basis and it cannot be intuitively
expected from all the agents to buy or sell an equal proportion of allowances. Gaussian or
the normal distribution seems to be most appropriate in this case and the results of these
experiments also confirm the same.
Table 5.5. Results of experiments for changing the proportion of
carbon assets
ECX CCX
Proportion of
carbon
allowances
Equal Gaussian Equal Gaussian
RMSE 0.032
(1)
0.089
(2)
0.064
(2)
0.029
(1)
MAE 0.013
(1)
0.056
(2)
0.073
(2)
0.038
(1)
Figures in parentheses indicate ranking of forecasting accuracy
91
5.8.3 Changing N
The results of experiments performed for number of agents N are given in Table 5.6 for
the simulated market of European Climate Exchange (ECX) and in Table 5.7 for the
simulated market of Chicago Climate Exchange (CCX). Keeping in view the results of
first two experiments, initial wealth distribution is kept as Maxwell-Boltzmann for both
the markets; and allowance proportion is kept as equal for the artificial market of ECX
and Gaussian for the artificial market of CCX.
From Table 5.6 relating to artificial carbon market of ECX, it is apparent that forecasting
performance using both the measures of accuracy improves continuously with the
increase in number of agents. As EU carbon market is in practice since 2003 and due to
fixation of emission reduction targets and the stringent implementation of rules in
Europe, the number of agents have increased to a considerably high level. As a result,
forecasting accuracy of agent based model is also the highest, when we consider their
number N as 100000. This is a positive indication for forecasting of compliance carbon
market for future also, as more and more agents are getting involved in the process of
carbon trading.
From table 5.7, for Chicago carbon market, the results depict that forecasting accuracy
improves first, as N is increased from 5000 to 25000; however, the same decreases
continuously as we further increase N to 50000 and finally to 100000. These results
again appear to mimic reality of Chicago market, which is a voluntary market so far and
Table 5.6. Results of experiments for changing N in ECX
N=5000 N=25000 N=50000 N=100000
RMSE 0.097
(4)
0.068
(3)
0.013
(2)
0.002
(1)
MAE 0.059
(4)
0.037
(3)
0.008
(2)
0.004
(1)
Figures in parentheses indicate ranking of forecasting accuracy
92
number of participants, who make investment in the same, is neither too small nor too
big.
Table 5.7. Results of experiments for changing N in CCX
N=5000 N=25000 N=50000 N=100000
RMSE 0.085
(3)
0.027
(1)
0.054
(2)
0.098
(4)
MAE 0.062
(2)
0.043
(1)
0.067
(3)
0.120
(4)
Figures in parentheses indicate ranking of forecasting accuracy
5.8.4 Comparison with analytical models
Preceding discussion focused on the capabilities of agent based models in forecasting
carbon markets and experiments to improve accuracy of results. However, from an
investor’s point of view, it would be advisable to draw a comparison between the agent
based models and analytical models for forecasting purposes. In Chapter 4, it was proved
that GARCH (1, 1) and non-linear GARCH models give maximum accuracy for
forecasting the spot markets of ECX and CCX, respectively. Hence in this section, a
comparison of agent based model and the respective analytical model is made for both
the markets.
First, the forecasting of ECX spot market is done with GARCH (1, 1) model given.
GARCH (p, q) process is defined as
tttr εσ= ; ∑∑ = −
=
−− ++=Ω≡p
j jtj
q
i
itittt uuE1
2
1
2
01
22 )( σδαασ (5.15)
where 1⟨+ δα and δj > 0 for all j=0,1,….p.
93
Forecasting accuracy is derived using both RMSE and MAE and the results are given in
the first column of Table 5.8. In second column the forecasting results from agent based
model in Table 5.4 are reproduced for comparison.
Table 5.8. Results of forecasting ECX spot market with GARCH
(1, 1) and ABM
GARCH (1, 1) Agent based model
RMSE 0.378 0.092 (4.1)*
MAE 0.213 0.075 (2.8)*
* indicates the number of times ABM is more accurate than GARCH (1, 1)
A comparison of the values in the two columns of Table 5.8, indicate that forecasting
accuracy of agent based model is higher than the corresponding analytical model for
ECX spot market.
Second, the forecasting of CCX spot market is done with non-linear GARCH model. N-
GARCH (1, 1), which is given as:
tttr εσ= ; 2
11
2
111
2
1101
22 )()( −−−− +++=Ω≡ tttttt HuuE σδσβαασ (5.16)
Where α1>0 and H1 is increasing function. Forecasting accuracy is again derived using
both RMSE and MAE and the results are given in the first column of Table 5.9. In second
column the forecasting results from agent based model for CCX in Table 5.4 are
reproduced for comparison.
A comparison of the values in the two columns of Table 5.8, indicate that forecasting
accuracy of agent based model is higher than the corresponding analytical model for
ECX spot market also.
94
Table 5.9. Results of forecasting CCX spot market with NL-
GARCH and ABM
NL GARCH model Agent based model
RMSE 0.575 0.086 (6.7)*
MAE 0.238 0.067 (3.5)*
* indicates the number of times ABM is more accurate than NL-GARCH
From both the tables 5.8 and 5.9, it is clear agent-based models have got more potential
for forecasting purposes than mathematical models used in finance. In addition, there is
no scope of improving forecasting accuracy in traditional econometric models. However,
in agent based models, by varying the model parameters and agents’ characteristics by
way of experimentation, forecasting accuracy can be considerably increased; which
means that artificial carbon markets simulated by means of agent based models can be
made to mimic real world markets as close as possible.
5.9 Summary and conclusions
One of the major challenges for carbon market investors is to understand and forecast the
prices of carbon assets. However due to involvement of various heterogeneous agents in
the market mechanism, standard analytical models do not seem to provide reliable
forecasting tools. A solution to this problem is found in the world of agent based models.
A genetically-programd agent based model is found to satisfy the stylized facts of the
compliance market of European Climate Exchange (ECX) and the voluntary carbon
market of Chicago Climate Exchange (CCX). Further, the forecasting capabilities of
agent based models are found to be considerably better than the analytical models. This
could be due to the fact that behavior of heterogeneous trading agents in incorporated
well in these models, which is not possible in the traditional mathematical models. In
traditional models, there is no scope of improving forecast accuracy. However, in agent
based models, it is considerably improved by changing model parameters and agent
characteristics by way of experimentation. Three model parameters are changed: wealth
95
distribution of agents; distribution of carbon assets as proportion of their total wealth; and
the number of agents in the artificially generated markets of ECX and CCX. Forecast
accuracy is found to increase considerably, when the parameter distributions or values are
close to the real market situations.
These results indicate that agent based models provide a very promising tool to
understand the price dynamics in carbon markets and obtaining high accuracy forecasts
as compared with the traditional econometric models. This study further opens doors to
many research directions. Carbon markets are a recent phenomenon and more and more
carbon markets are coming up in all parts of the world. One obvious extension of this
work is to apply agent based model to other markets for forecasting as the new data
becomes available from different parts of the world. Some of the most challenging
research concerns microstructure of carbon markets (Madhavan 2000), which could be
studied within artificial carbon markets. Going further, different groups of carbon market
participants like electric utilities, forest owners and transporters etc. can be clubbed
together and inter-group dynamics of market can be explored. In addition, the behavior of
fundamental trading agents can also be incorporated using the data of marginal abatement
cost from various industries. In addition, the experiments in this study have focused so far
on three parameters only, keeping others fixed. Future work may also include variations
in other parameters also, so as to have a bigger picture on the market behavior in carbon
trading. Nonetheless, the experiments carried out in this chapter being of pioneering
nature can work as a starting platform for further research in the use of agent based
models in understanding and forecasting of carbon markets in the times to come. Apart
from these issues, only price variable has been included in this chapter due to data and
software limitations. With advancements in the available softwares in the near future,
volume variable can also be included. Similarly efforts could be directed towards
incorporating policy level decisions in the model to incorporate strategic variables in the
model. Quoting LeBaron (2000), “this field is only in its infancy and much remains to be
done”, further improvements could be made in computation capabilities also by making
use of high level programming codes in high level languages, for example, Java and C++,
to have a better picture about use of agent based models in CO2 emission trading markets.
96
6 Conclusions, Policy Implications, Limitations and Future Work
6.1 Conclusions
Forests play a major role in setting the CO2 levels in the atmosphere through carbon
sequestration. Carbon markets are one of the most innovative and cost-effective means of
creating a market pull for forestry credits generated through afforestation and
conservation activities. Due to increase in quantum of carbon trading over last few years,
various issues related to price dynamics of carbon markets have arisen in the recent past.
First, carbon markets have emerged at regional, national and international levels and are
governed by specific demand and supply patterns. There is a need to unify these markets
to increase overall carbon market efficiency. Second issue relates to understanding of
short-run volatility of carbon markets, as forecasts of carbon price volatility could be
important inputs into macro-econometric models and market risk assessment calculations
like value at risk and; for the choice of a carbon policy instrument. Third, carbon markets
consist of various heterogeneous agents such as greenhouse gas emitters, agriculturists,
foresters and individual market investors. These agents interact with each other and with
the overall trading-environment to evolve the emergent behavior of these markets.
Traditional approach for study of price dynamics in such markets is through use of
analytical models that assume completely rational agents. This causes biased results and
lesser forecast accuracy. To improve forecast accuracy, there is a need to carry research
on incorporating agent heterogeneity and limited rational behavior.
This research is therefore carried out in the form of three essays and economic analyses
are conducted on world’s carbon markets to examine these issues. Both compliance
markets of EU and voluntary market of North America have been covered in analyses.
The first essay addresses long-run integration of carbon markets at the interregional level
using Johansen full information maximum likelihood procedure for testing co-integration.
The second essay evaluates the performance of various econometric models for
predicting price volatility of carbon in different markets. In the third essay, an agent
based model of carbon markets is analyzed and the statistical properties of the artificially
simulated carbon markets are explored. The agents are sophisticated genetic
97
programming based computer programs that co-evolve with learning by predicting
investment opportunities in the market using technical analysis as the main tool.
Experiments are performed on endogenous artificial markets to improve forecasting
accuracy of the model. The major conclusions of these analyses are:
First, the allowance-based carbon markets across North America and EU are not
cointegrated. A possible cause could be the fact that in EU countries, carbon market
investments take place on account of compliance under Kyoto targets; whereas in North
America, investors are trading in carbon markets purely on account of their
environmental responsible behavior or for anticipated fixation of targets in future. In
addition, international protocols like the Marrakesh Accords require that for compliance
purposes in EU, carbon credits could be used only from the Kyoto signatory nations,
which excludes the US based carbon markets. Due to lack of cointegration between EU
and North American carbon markets, an overall inefficiency is introduced in the system
and emissions cannot be reduced at the least possible cost.
Second, allowance-based markets within North America are cointegrated with each other.
This implies a common stochastic trend in the North American carbon market and could
be the result of spatial proximity and uniform regulatory mechanism so far. This common
trend could bind all these markets together and forecasting of prices in any of these
markets can be enhanced significantly by utilizing information from the prices of another
one. The traders, on account of perfect information, can gain potentially through
equalizing transaction costs in the unified North American carbon market. However,
recently, within North-American carbon markets, there is an indication of switching of
some buyers, specifically Canadian buyers, from the US markets to the Canadian market
due to establishment of Montreal exchange, as the firms now have an option to trade in
either of them. In the long-run equilibrium, if more firms trade in the US markets, leading
to increase in prices in the US markets, the Canadian market will face less demand and
therefore prices will decrease or vice-versa.
Third, CDM project based CER markets in Europe and USA are cointegrated because of
the fact that these credits are generated primarily in the developing countries and
98
irrespective of the trading countries; their prices show co-movement around the world.
This indicates efficiency and existence of a global carbon market for CDM projects.
Looking at the specifics, the types of projects eligible for generating CERs in ECX and in
CCX are not similar. As a result, the situation market might change in future, if attempts
are not made either to link or to make both the markets homogenous with respect to type
of projects. Nonetheless, the development of global carbon market for CDM can be seen
as one manifestation of improved expectations for ensuring carbon sequestration and
sustainable development in the developing countries.
Fourth, for future, it is expected that new carbon markets coming up in different parts of
the world such as Australia, China, India and other countries, might not be co-integrated.
Such phenomenon could be due to different compliance requirements for different
countries and regions under international protocols, different sets of institutional
arrangements at the local levels, different expectation levels for environmental
sustainability and also due to restrictions on participation of buyers from other countries
and regions. The possibilities of arbitrage across the global markets will hence be limited,
and the carbon trading in these markets are expected to be globally inefficient in future.
Therefore, there is a strong need of a global agreement that allows global carbon trade to
prevent climate change at the least cost options.
Fifth, voluntary market of Chicago is more volatile than the compliance market of EU.
However, despite the various policy level changes, the time-series data for short term
volatility in both the markets follow a stationary pattern and hence volatility can be
forecasted for both of them. This could be helpful for carbon market investors, as they are
trading on the basis of daily price fluctuations, which are represented best by the
volatility.
Sixth, different carbon markets witness different volatility patterns and hence separate
econometric models are required for forecasting volatility for each of these markets. The
volatility behavior of voluntary market of Chicago is quite similar to that of other
financial markets and energy markets like oil and natural gas, which are all forecasted
well by complex non-linear GARCH models. Whereas, simple models like Historical
99
averages and GARCH (1, 1) perform the best for compliance bound EU market, thereby
indicating different behavior of compliance carbon market from the voluntary carbon
market and other financial and energy markets.
Seventh, genetically programd agent-based models have considerable potential in
understanding the price dynamics of CO2 emission trading markets. These models
possess much better forecasting capabilities than the traditional econometric models. The
artificial carbon markets obtained from such agent based models generate features which
are remarkably similar to those from the actual data. Experiments performed on
artificially simulated carbon markets show that changing parameters of the model could
be adjusted to further increase the forecast accuracy, which is not possible in the world of
analytical models.
6.2 Policy Implications
Some policy implications are drawn from these analyses:
First, the effects of inter-continental CO2 allowance trade, particularly across Atlantic are
limited so far, and hence the market power1 of regional credit suppliers is large (Vatiero
2010). An important policy intervention could be to allow establishing links between
different countries, irrespective of their Kyoto commitments to tackle climate change
through use of markets. It will provide better opportunities to the traders and also result in
unification of allowance prices in the two continents. The result could also be used for
convincing the North American countries to fix emission reduction targets, as it will
bring efficiency in overall global carbon trading mechanism.
Second, as the CDM project markets are cointegrated and reflect efficiency, a policy
level decision could be taken to boost the CER market to further promote the CDM
projects, as they have an additional virtue of ensuring sustainable development in the
1 Market power is the ability of a firm to alter the market price of a good or service. In perfectly
competitive markets, market participants have no market power.
100
developing countries. Developed countries should continue to improve the investment
environment and enhance incentives for these projects in the developing world.
Third, markets which are not integrated show inefficiencies and policy level changes are
required in the structure and design of the individual trading schemes. A policy level
initiative would be to link such emission trading mechanisms so as to integrate them in
the long run.
Fourth, understanding the short-term volatility dynamics might enable companies to
monitor the costs of CO2 emissions in their production process. At firm level, it could be
useful in deciding about banking and borrowing of the carbon credits as these options
allow firms to smooth emissions over time, which in turn smoothes the price of
allowances and increases certainty and thus investment.
Fifth, the study of volatility dynamics may be helpful in choosing between carbon tax and
the market based instruments at the policy level. Drawing comparisons between the
forecasts of various carbon markets with expected returns from a carbon tax, the policy
makers can have a choice to go for either or a mix of the two. Knowledge of volatility
behavior in different markets also presents policy makers an ability to choose from
different mechanisms to reduce uncertainties: To allow banking of allowances for future
use for motivating firms to further reduce their emissions now by allowing them to
establish a reserve for the future; or to allow firms to borrow allowances from future
periods; or to set price floor and/or ceiling to reduce the risks to investments in emission
reductions.
Lastly, the agent based models could be used to draw comparison between not only the
price dynamics, but also for choice of policy instruments, as they are shown to possess
better forecasting capabilities through incorporation of agent behavior, heterogeneity and
limited rational behavior.
6.3 Limitations and Future Work
While economic analyses in this research provide useful results related to price dynamics
of world carbon markets, they suffer from some limitations.
101
First, the number of co-integrated markets is not a true measure of the degree of market
integration; that can be only assessed by measuring the reaction time to remove
disequilibria from the cointegrating relationships. Similarly, Johansen’s multivariate
cointegration procedure does not take into account the transaction costs, the marginal
abatement costs and other charges associated with carbon trading; and therefore is not a
very reliable method for analyzing the efficiency of arbitrage between the two markets. In
addition, only univariate price equations have been considered, whereas, volume of
trading can also be taken into account while exploring market integration. Future research
should include more assets from other carbon markets of the world and the enhanced
aspects of market integration. New research should not only confirm or contradict the
present results, but also try to resolve such issues by using further econometric analysis
and looking at more recent developments in the international carbon markets using more
extensive data series coming from newly emerging carbon markets.
Second, this dissertation is one of the pioneering studies pertaining to economics of
world’s carbon markets and hence is limited to examination of only price variable. All
the models considered belong to the univariate time-series family of carbon prices, and
examination of multivariate models that may include traded volume might bring some
changes in the results. Environmental variables like weather patterns and financial
variables like the number and type of listed companies on the climate exchanges and
policy issues like mandatory fixing of emission reduction targets by the federal or
provincial governments in the EU and US can further improve the accuracy of results.
Third, different carbon markets became functional at different points of time and hence
slightly different time horizons have been used in all the analyses. Accuracy of results
might improve after passage of more time, as the markets get mature.
Fourth, more trading options have been introduced recently in both EU market and in
Chicago Climate Exchange. An array of additional financial instruments-options,
derivatives and swaps are becoming available in different carbon markets around the
world. Their comparison will be desirable in future to get a more comprehensive picture
of the world carbon markets.
102
Fifth, an extension of agent based model could be made to other carbon markets for
forecasting as the new data becomes available from different parts of the world. Different
groups of carbon market participants like electric utilities, forest owners and transporters
etc. can be clubbed together and inter-group dynamics of market can be explored. In
addition, the behavior of fundamental trading agents can also be incorporated using the
data of marginal abatement cost from various industries. Experiments on artificial
markets have focused so far on three parameters only, keeping others fixed. Future work
may also include variations in other parameters also, so as to have a bigger picture on the
market behavior in carbon trading. Similarly efforts could be directed towards
incorporating policy level decisions in the model to incorporate strategic variables in the
agent based model. Further improvements could also be made in computation capabilities
also by making use of high level programming codes in high level languages, for
example, Java and C++, to have a better picture about use of agent based models in CO2
emission trading markets.
Lastly, no structural breaks have been observed in data in most of the data, which shows
that policy level changes so far did not have very significant effect on the price dynamics
of these markets. However, with significant policy level changes at Copenhagen and
Cancun meets of UNFCCC, some structural breaks may arise in data in future, which
needs to be taken into account for further analysis.
103
References
Akgiray, V. 1989. Conditional heteroskedasticity in time series of stock returns: Evidence and forecast, Journal of Business, 62, 55-80
Alfi, V., Pietronero, L. and Zaccaria 2009. Self-organization for the stylized facts and finite-size effects in a financial market model, EPL, 86
Anger, N. 2008. Emissions trading beyond Europe: Linking schemes in a post-Kyoto world, Energy Economics, 30, 2028-2049
Armstrong, J.S., Fildes, R. 1995. On the selection of error measures for comparisons among forecasting methods, Journal of Forecasting, 14, 329-52
Arthur, W.B., Holland J.H., LeBaron, B., Palmer, R.G. and Tayler, P. 1997. Asset pricing under endogenous expectations in an artificial stock market, in The Economy as an evolving complex system II, Reading: MA: Addison-Wesley
Axelrod R., Tesfatsion, L. 2005. A guide for new comers to agent based modeling in the social sciences, Gerald R. Ford School of Public Policy, University of Michigan
and Economics Department, Iowa State University, Ames, IA, 1-13
Balaban, E., Bayar, A., Faff, R. 2006. Forecasting stock market volatility, Further international evidence, The European Journal of Finance, 12, 2, 171-188
Banerjee, A., Dolado, J., Galbriath, J. and Hendry, D. 1993. Cointegration, error correction and the economic analysis of non-stationary data, Oxford University Press Inc. 329
Bayon, R., Hawn, A., Hamilton, H. 2007. Voluntary carbon markets- An international guide to what they are and how they work, Earthscan Sterling VA, 50-66
Benz, E., Trück, S. 2006. CO2 emission allowances trading in Europe- specifying a new class of assets, Problems and Perspectives in Management, 3
Benz, E., Trück, S. 2009. Modelling the price dynamics of CO2 emission allowances, Energy Economics, 31, 4-15
Bodie, Z., Kane, A., Marcus, A.J., Perrakis, S., Ryan, P.J. 2010. Investments, McGraw-Hill Ryerson, Toronto
Bohringer, C., Hoffman, T., Manrique-de-Lara-Perate, C. 2006. The efficiency costs of separating carbon markets under the EU emissions trading scheme: A quantitative assessment for Germany, Energy Economics, 28, 44-61
Bollersev, T., 1986. Generalised autoregressive conditional heteroskedasticity, Journal of
Econometrics, 31, 307-27
Brailsford, T.J. and Faff, R.W. 1996. An evaluation of volatility forecasting technique, Journal of Banking and Finance, 20, 419-38
Brenner, T. 2005. Agent learning representation—advice in modeling economic learning, Handbook of Computational Economics, Volume 2: Agent-Based Computational
Economics, Judd, K. and Tesfatsion, L. Eds. New York: Elsevier
104
Brock, W., Lakonishok, J., LeBaron, B. 1992. Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance, 47, 1731–1764
Brohe, A., Eyre, N., Howarth, N. 2009. Carbon markets: An international business guide, Earthscan Sterling VA, 51-53
Brooks, C. 1998. Predicting stock index volatility: Can market volume help? Journal of
Forecasting, 17, 59-80
Burtraw, D. 1996. Cost savings sans allowance trades? Evaluating the SO2 emission trading program to date, Discussion Paper, 95-30
Capoor, K., Ambrosi, P., 2009. State and trends of the carbon markets, World Bank climate change team, Washington D.C. 1-50
CCAR 2010 California Climate Action Registry, http://www.climateregistry.org/about.html, downloaded on 30th December 2010, 1-2
CCX 2010 Chicago Climate Exchange www.chicagoclimatex.com/market/data/daily.jsf, downloaded on 30th December 2010, 1-2
Chen, S.-H. and Yeh, C.-H. 2001. Evolving traders and the business school with genetic programming: A new architecture of the agent-based artificial stock market, Journal of Economic Dynamics and Control, 25, 363–393
Chao, H.P., Wilson, R. 1993. Option value of emission allowances, Journal of
Regulatory Economics, 5, 233-49
Chueng, Y.W., Lai, K.S. 1993. Finite sample sizes of Johansen’s likelihood ratio tests for cointegration. Oxford Bulletin of Economics and Statistics, 55, 3, 313-328
Christoffersen, P.F., Diebold, F. 1987. Optimal prediction under asymmetric loss, Econometric Theory, 13, 808-17
Convery, F.J., Redmond, L. 2007. Market and price developments in the European Union Emissions Trading System, Review of Environmental Economics and Policy, 1, 88-111
CoP. 2009. Conference of the Parties, United Nations Framework Convention on Climate Change, Copenhagen, Fifteenth session, Agenda Item 9
Daskalakis, G., Psychoyios, D., Markellos, R. 2005. Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme, Journal of
Banking and Finance 33, 1230-1241
Davidson, R., Mackinnon, J.G. 2004. Econometric theory and methods, Oxford University Press, New York, 587-589
Dejong, D.N., J.C. Nankervis, J.S. and Savin, N.E. 1992. Integration versus trend stationarity in time series, Econometrica, 60, 423– 433
Dempster, M. A. H., Payne, T.W., Romahi, Y. and Thompson, G. W. P. 2000. Computational learning techniques for intraday FX trading using popular technical indicators, IEEE Transactions in Neural Networks, 12, 744–754
105
Dickey, D.A., Fuller, W.J. 1979. Distribution of estimates for autoregressive time-series with unit root, Journal of American Statistics Association, 74, 427-431
Dimson, E., Marsh, P. 1990. Volatility forecasting without data-snooping. Journal of
Banking and Finance 14, 399-421
Ding, Z., Engle, R., Granger, C., 1993. A long memory property of stock market returns and a new model. Journal of Empirical Finance 1, 83-106
ECX. 2010. European climate exchange futures and options market www.ecx.eu/media/xls/ecx%20eua %20futures%20contract%20- %2031%20july%202009.xls and www.ecx.eu/media/xls/ecx%20eua %20options%20contract%20-%2031%20july%202009.xls, downloaded on 30th December 2010, 1-2
Edmonds, B., Moss, S. 1997. Modelling bounded rationality using evolutionary techniques, Proceedings in Evolutionary Computing, AISB Workshop, 31–42
Edmonds, B. 1999. Modelling bounded rationality in agent-based simulations using the evolution of mental models, in Computational Techniques for Modelling Learning
in Economics, Brenner, T., Ed. Norwell, MA: Kluwer, 305–332
Egert, B., and Kocenda, E. 2007. Interdependence between Eastern and Western European stock markets: Evidence from intraday data, Economic Systems, 31, 184-203
Elliot, G., Rothenberg, T.J. and Stock, J.H. 1996. Efficient tests for an autoregressive unit root, Econometrica, 64, 813– 836
Engle, R., and Granger, C.W.J. 1987. Co-integration and error correction: Representation, estimation and testing, Econometrica, 55, 251–276
Engle, R.F. 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007
Fankhauser, S. 1994. The social costs of greenhouse gas emissions: An expected value approach, Energy Journal, 15, 2, 157-184
FAO. 2011. Climate Change, Food and Agricultural Organization, http://www.fao.org/climatechange/en/, downloaded on 15-03-2011, 1-12
Farber, S.C., Costanza, R., Wilson, M.A. 2002. Economic and ecological concepts for valuing ecosystem services, Ecological Economics, 41, 375-392
Farmer, J.D. 1998. Market force, ecology, and evolution, Industrial and Corporate
Change, 11, 895–953
Flachsland, C., Marschinski, R., Edenhofer O. 2009. To Link or Not to Link: Benefits and Disadvantages of Linking Cap-and-Trade Systems, Climate Policy, 9, 4, 358-372
Florus, C., and Vougas, D. 2008. The efficiency of Greek stock index futures market, Managerial Finance 34, 7, 498-519
106
FRSR. 2010. Federal Reserve Statistical Release, H.10. Foreign Exchange Rates, USA, http://www.federalreserve.gov/releases/h10/Hist/ downloaded on 15th February 2010, 1-4
Garcia-Almanza, A. L. and Tsang, E. P. K. 2006. Simplifying decision trees learned by genetic algorithms, Proceedings IEEE World Congress Computational
Intelligence
Garnaut, R. 2008. Garnaut climate change review, Interim report to the Commonwealth, state and territory Governments of Australia, 1-43
Grossman, S. and Stiglitz, J. 1980. On the impossibility of informationally efficient markets, American Economic Review, 70, 393-408
Gonzalo, J. 1994. Five alternative methods of estimating long-run equilibrium relationships, Journal of Econometrics, 60, 203–233
Hafer, R.W., Sheehan, R.G. 1991. Policy inference using VAR models, Economic
Inquiry, 29, 1, 44-52
Haites, E., Wang, X. 2009. Ensuring the environmental effectiveness of linked emission trading schemes, Mitigation Adaptation Strategic Global Change, 14, 465-476
He, Y., Wang, S. and Lai, K.K. 2010. Global economic activity and crude oil prices: A cointegration analysis, Energy Economics, xxx, xxx-xxx
Held, H., Edenhofer, O. 2008. Climate protection vs. economic growth as a false trade- off: Restructuring global warming mitigation. Handbook of Transdisciplinary Research, Springer, Verlag, 191
Harris, R., and Sollis, R. 2003. Applied time series modeling and forecasting, John Wiley and Sons Ltd., New York, 320
Hänninen, R. 1998. The law of one price in United Kingdom soft sawn wood imports:A cointegration approach, Forest Science, 44, 17-23
Hentschel, L.F. 1995. All in the family: nesting linear and non-linear GARCH models, Journal of Financial Economics, 39, 139-164
Hight, C. and Silva-Chavez, G. 2008. Change in the air: The foundations of the coming American carbon market, Climate Report, 15
Hoffman, M.J. 2006. Beyond regime theory: Complex adaptation and global environmental governance, in global complexity: Agent-based models in global and international issues, edited by Neil Harrison, SUNY Press, 1-16
IPCC. 2007. Fourth Assessment Report, Intergovernmental Panel on Climate Change, 5-15
Jang, H., Sul, W. 2002. The Asian financial crisis and co-movement of Asian stock market, Journal of Asian Economics, 13, 94-104
Johansen, S. 1988. Statistical analysis of cointegrating vectors, Journal of Economic
Dynamics and Control, 12, 231-254
107
Johansen, S. 1995. Likelihood-based inference in co-integrated vector autoregressive models. Oxford University Press, New York, 267
Johansen, S. and Juselius, K. 1990. Maximum likelihood estimation and inference on co-integration, with applications to the demand for money, Oxford Bulletin of
Economics and Statistics, 52, 169 –210
Johansen, S. and Juselius, K. 1992. Structural tests in a multivariate cointegration analysis of the PPP and the UIP for UK, Journal of Econometrics, 53, 211–244
Johansen S. 2002. The interpretation of cointegrating coefficients in the cointegrating vector regression models, Department of Theoretical Statistics, University of Copenhagen, 1-13
Jung, C., Doroodian, K. 1994. The law of one price for U.S. softwood lumber: A multivariate cointegration analysis, Forest Science, 40, 4, 595-600
Kang, S.H., Kang, S-M., Yoon, S-M. 2009. Forecasting volatility of crude oil markets. Energy Economics, 31, 119-125
Karmali, A. 2010 Observations from the carbon emission markets: Implications for carbon finance, Book Chapter in Sustainable Investing: The art of long-term performance, edited by Krosinsky, C. and Robins, N. Earthscan, London, 61-62
Kasa, K. 1992 Common Stochastic Trends in International Stock Markets, Journal of Monetary
Economics 29, 95-124
Kaufmann, S., Scheicher, M. 2006. A switching ARCH model for German DAX index, Studies in
Non-linear Dynamics and Econometrics, 10, 4, 1-35
Keohane, N.O. 2009. Cap and Trade, Rehabilitated: Using tradable permits to control U.S. greenhouse gases 3, 1, 42-62
Kossoy, A., Ambrosi, P. 2010. State and trends of the carbon market, World Bank, Washington DC, 1-62
Kruger, Oates and Pizer, 2007. Decentralization in the EU emissions trading scheme and lessons for global policy, Discussion Paper, Resources for the future, 1-34
Koza, J.R. 1992. Genetic Programming: On the programming of computers by means of natural selection, The MIT Press, Cambridge, 73-79
Labatt, S. and White, R. 2007. Carbon Finance: The financial implications of climate change. John Wiley and Sons, Inc Hoboken, New Jersey, 8-11
Laurendeau, N. M. 2003. Statistical thermodynamics: fundamentals and applications, Cambridge University Press, 434
LeBaron, B., Arthur, W.B. and Palmer, R. 1998. Time series properties of an artificial stock market, Journal of Economic Dynamics and Control, 23, 1487-1516
LeBaron, B. 2000. Building financial markets with artificial agents: Desired goals, and present techniques, Computational Markets, Karakoulas, MIT Press
108
LeBaron, B. 2001. A builder’s guide to agent based financial markets, Quantitative
Finance, 1, 254–261
Linacre, N., Kossoy, A., Ambrosi, P. 2011. State and trends of the carbon market, World Bank, Washington DC, 1-84
Lucas, R. E. 1986. Adaptive behavior and economic theory, Rational Choice: The Contrast Between Economics and Psychology, R.M. Hogarth and M. W. Reder, Eds. Chicago, IL: Univ. Chicago Press, 217–242.
L¨utkepohl, H. 1993. Introduction to multiple time series analysis, Springer-Verlag, Heidelberg, 14-19
L¨utkepohl, H. and Saikkonen, P. 1999. Order selection in testing for the cointegration rank of a VAR process. In Cointegration, causality, and forecasting—A Festschrift in Honour of Clive W.J. Granger, Engle, R.F., and H. White (eds.). Oxford University Press, Oxford, UK
Lux, T. 1998. The socio-economic dynamics of speculative markets: Interacting agents, chaos, and the fat tail distributions, Journal of Economic Behavior and Finance, 33, 143-165
Maddala, G.S., Kim, I.-M. 1998. Unit roots, co-integration, and structural change, Cambridge University Press, 505
Madhavan, A. 2000. Market microstructure: A survey, Journal of Financial Markets 3, 205-258
Maghyereh, A., Kandari, A. 2007. Oil prices and stock markets in GCC countries: new evidence from nonlinear cointegration analysis, Managerial Finance 33, 7, 449-460
Majid, M.S.A., Meera, A.K.M., Omar M.A. 2008 Interdependence of ASEAN-5 stock markets from the US and Japan, Global Economic Review, 37, 2, 201-225
Malmsten, H., Teräsvirta, T. 2004. Stylized Facts of Financial Time Series and Three Popular Models of Volatility: Working Paper Series in Economics and Finance 563, Stockholm School of Economics
Marcu A. 2006. The business case. Environmental Finance, May. Supplement: Global Carbon, S8-S9
Martinez-Jarmillo, S. and Tsang, E.P.K. 2009. An heterogenous, endogenous and coevolutionary GP-based financial market, IEEE Transactions on Evolutionary
Computation, 13, 1
Mandelbrot, B. B. 1963. The variation of certain speculative prices, Journal of financial
Business 36, 394–419
Mantegna, R.N. and Stanley, H.E. 2000. Introduction to Econophysics: Correlations and complexity in finance, Cambridge University Press, Cambridge
Markose, S., Tsang, E.P.K., Martinez-Jaramillo, S., Angeline, P.J., Michalewicz, Z., Schoenauer, M., Yao, X. and Zalzala, A. 2003. The Red Queen principle and the
109
emergence of efficient financial markets: An agent based approach, Proceedings 8th Workshop on Economic Heterogeneous Interacting Agents (WEHIA), Kiel, Germany, 2, 1253–1259
Masih, A.M.M., Masih, R. 1999 Are Asian Stock Market Fluctuations Due Mainly to Intra-Regional Contagion Effects? Evidence Based on Asian Emerging Stock Markets, Pacific-Basin Finance Journal, 7, 251-282
MCeX. 2010. Montreal Climate Exchange, http://mcex.ca/aboutUs_overview_en, downloaded on 15-11-2010
Mehling, M., Haites, E. 2009. Mechanisms for linking emission trading schemes. Climate
Policy, 9, 169-184
Merton, R. 1980. On estimating the expected return on the market: An explanatory investigation, Journal of Financial Economics, 8, 323-61
Michelfelder, R.A. 2005. Volatility of stock returns: Emerging and mature markets, Managerial Finance, 31, 2, 66-86
Mizuta, H. and Yamagata, Y. 2005. Gaming simulation of the international CO2 emission trading under Kyoto Protocol, Agent-Based Simulation: Post proceedings of the third international workshop on agent-based approaches in economic and social complex system, JPN: Springer-Verlag, 72-81
Morgan, M. 2008. Trading carbon financial instruments contracts on CCX and CCFE: Cash, futures and options. http://www.chicagoclimatex.com/images/content/File/Trading_CFIs.pdf, downloaded on 20/03/2009
Moroza, J. 2008. Dynamic linkages between Baltic and international stock markets, M.Sc. Thesis, School of Economics and Management, Lund University, Sweden, 1-50
Moshiri, S., Foroutan, F. 2006. Forecasting nonlinear crude oil future prices, Energy Journal, 27, 4, 81-95
Nelson, D.B. 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59, 347-370
Neely, C. J., Weller, P. and Dittmar, R. 1997. Is technical analysis in the foreign exchange market profitable? a genetic programming approach, Financial and
Quantitative Analysis, 32, 405–426
Ng, S., and Perron, P. 1995. Unit root tests in ARMA models with data dependent methods for the truncation lag, Journal of American Statistics Association, 90, 268 –281
Nichols, M.D. 2009. California’s climate change program: Lessons for the nation, Journal of Environmental Law and Policy, 185, 186-209
Nordhaus, W.D. 1991. To slow or not to slow: The economics of the greenhouse effect, Economic Journal 101, 920-937
110
Nordhaus, W.D. 2007. To tax or not to tax: Alternative approaches to slowing global warming, Review of Environmental Economics and Policy, 1, 26-44
Oberndorfer, U. 2008. EU emissions allowances and the stock market: Evidence from electricity industry, Ecological Economics, 68, 1116-1126
Pagan, A., Schewart G.W. 1990. Alternative models for conditional stock volatilities, Journal of Econometrics, 45, 267-90
Paolella, M.S., Taschini, L., 2008. An econometric analysis of emission allowance prices, Journal of Banking and Finance, 32, 2022-2032
Palmer, R. G., Arthur, W. B., Holland, J. H., LeBaron, B. and Tyler, P. 1994. Artificial economic life: A simple model of a stock market, Physica, 75, 264–274
Penzer, J. 2009. Approximating volatilities by asymmetric Power GARCH functions. London School of Economics, 1-4.
Perron, P. 1989a. Testing for a random walk: A simulation experiment of power when the sampling interval is varied, 47–68, Advances in Econometrics and Modeling, Raj, B. (ed.). Kluwer Academic Publishers, Dordrecht, The Netherlands
Perron, P. 1989b. The great crash, the oil price shock and the unit root hypothesis. Econometrica, 57, 1361–1401
Perron, P. 1994. Trend, unit root and structural change in macroeconomic time series, 113–146, Cointegration for the applied economist, Rao, B.B. (ed.). Macmillan Press, Basingstoke, UK.
Perry, P., 1982. The time-variance relationship of security returns: Implications for the return-generating stochastic process, Journal of Finance, 37, 857-70.
Persson, T.A. 2009. Linking to the Northeast states of the US mitigation program to the EU emission trading scheme-Implications and costs, Adaptation and Mitigation
Strategies for Global Change, 14, 399-408
Phillips, P.C.B., Perron, P. 1988. Testing for a unit root in time series regression, Biometrika, 75, 335-46
PointCarbon. 2004. Special issues: what determines the price of carbon? Carbon Market
Analyst, 14-19
PWC. 2010. Climate principles progress review, PricewaterhouseCooper, www.pwc.com, downloaded on 25-12-2010, 1-4
Raberto, M., Teglio, A. and Cincotti, S. 2008. Integrating real and financial markets in an agent-based economic model: An application to monetary policy design, 1-14
Raufer, R.K., Feldman, S.L. 1987. Acid rain and emissions trading: Implementing a market approach to pollution control, Rowman and Littlefield, New Jersey, 12-19
Roh, T.H. 2007. Forecasting the volatility of stock price index, Expert Systems with
Applications, 33, 916–922
111
Sadorsky, P. 2006. Modeling and forecasting petroleum futures volatility. Energy
Economics 28, 467-488.
Seifert, J., Uhrig-Homburg, M., Wagner, M. 2008. Dynamic behavior of CO2 spot prices, Journal of Environmental Economics and Management, 56, 180-194.
Sentana, E. 1995. Quadratic ARCH models, Review of Economic Studies, 62, 639-61
Shahi, C., Kant, S., Yang, F. 2006. The law of one price in the North American softwood lumber markets, Forest Science, 52, 4, 2006
Skintzi, V., Xanthopouloussisinis, S., 2007. Evaluation of correlation forecasting models for risk management, Journal of Forecasting, 26, 497-526
Scheinkman, J.A., Woodford, M. 1994. Self-organized criticality and economic fluctuations, American Economic Review, 84, 417-421
Soleille, S. 2006. Greenhouse gas emission trading schemes: A new tool for the environmental regulators’ kit, Energy Policy, 34, 13, 1473-1477
Spash, C. 2002. Greenhouse Economics: Value and Ethics, Routeledge, London, 15-25
Stern, N. 2006. The economics of climate change, The Stern Review, Cambridge University Press, UK
Stoll, H.R., Whaley, R.E. 1993. Future and options: Theory and applications. South Western Publishing Co. Cincinatti, Ohio, 1-11.
Stanley, H.E., Amaral, L.A.N., Buldyev, S.V., Gopikrishnan, P., Plerou, V. and Salinger, M.A. 2002. Self-organized complexity in economics and finance, Proceedings of Natural Academy of Sciences USA 101, 2561-2565
Sterk, W., Kruger, J. 2009. Establishing a transatlantic carbon market, Climate Policy, 9, 389-401
Streck, C., Tuerk, A., Schlamadinger, B. 2009. Forestry offsets in emissions trading systems: a link between systems, Mitigation Adaptation Strategic Global Change, 14, 455-463
Su, Q., Chong, T. T-L., Yan, I. K-M. 2007. On the convergence of the Chinese and Hong Kong stock markets: a cointegration analysis of the A and H shares, Applied Financial
Economics, 17, 1349-1357
Tesfatsion, L. 2001. Guest editorial: Agent-based modeling of evolutionary economic systems, IEEE-EC 5, 437–441 Tesfatsion, L. 2005. Agent based computational economics: A constructive approach to economic theory, Economics Department, Iowa State University, Ames, IA, 1-55
Tsang, E. P. K. and Martinez-Jaramillo, S. 2004. Computational finance, IEEE
Computational Intelligence Society Newsletter, 3-8
Tseng, J.J., Lin, C.H., Lin, C.T., Wang, S.C. and Li, S.P. 2010. Statistical properties of agent-based models in markets with continuous double auction mechanism, Physica 389, 1699-1707
112
Uri, N.D., Boyd, R. 1990. Considerations on modeling the market for software lumber in the United States. Forest Science 36, 3, 680-692
Uhrig-Homburg, M., Wagner, M. 2007. Future price dynamics of CO2 emission certificates-An empirical analysis, Working Paper, Universität Karlsruhe, Germany
Valadkhani, A., Chancharat, S. 2008. Dynamic linkages between Thai and international stock markets, Journal of Economic Studies, 35, 5, 425-441
Veld, K.V., Plantinga, A. 2005. Carbon sequestration or abatement? The effect of rising carbon prices on the optimal portfolio of greenhouse gas mitigation strategies, Journal of Environmental Economics and Management, 50, 59-81
Vatiero, M. 2010. The Ordoliberal notion of market power: an institutionalist reassessment, European Competition Journal, 6, 3, 689-707
Wang, Y. and Lin, C. 2007. Forecasting volatility for the stock market: a new hybrid model, International Journal of Computer Mathematics, 11, 1697-1707
White House. 2009. Energy and the environment, www.whitehouse.gov/agenda/energy_and_environment, downloaded on 15-12-2010
White House. 2010. http://www.whitehouse.gov/, downloaded on 15-12-2010
Winker, P. and Gilli, M. 2001. Validation of agent-based models of financial markets, IFAC Modeling and Control of Economic Systems, 401-406
Witkam, J. 2010. Altreva Adaptive Modeler: User’s guide, 1-125
Wooldridge, J.M. 2006. Econometric analysis of cross section and panel data, Cambridge, Massachusetts, MIT Press
World Bank, 2008. Carbon Finance for sustainable development, World Bank, Washington D.C. 1-25
Yang, F., Kant, S., Shahi, C. 2006. Market performance of the government-controlled but market-based stumpage system of Ontario, Forest Science 52, 4, 367-380
Yeh, C.-H. and Chen, S.-H., 2000. Toward an integration of social learning and individual learning in agent-based computational stock markets: The approach based on population genetic programming, Proceedings 6th International Conference in Computational Economics, Barcelona, Catalonia, Spain
Yu, J., 2002. Forecasting volatility in the New Zealand stock market, Applied Financial
Economics, 12, 193-202
Zivot, E., and Andrews, D.W.K. 1992. Further evidence on the great crash, the oil-price shock, and the unit root hypothesis, Journal of Business Economics and Statistics, 10, 251–270
Zoellick, R.B. 2008. Bali Breakfast Series, UNFCCC, CoP-15, 1-15
113
Appendix-1
Fig. A1. Genetic Programming Flowchart, adopted from Koza (1992)