john putney

8/12/2019 John Putney

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Valuation Challenges for Real World

Energy Assets

Dr John PutneyRWE Supply and Trading


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RWE Supply & Trading 7/20/2014 PAGE 2

Contents

> Typical energy assets gas swing, gas storage, power plants

> Valuing energy assets in traded markets

> Classic valuation models intrinsic and stochastic

> Where classic models fall short

> An alternative approach - methodology and infrastructure

> Building a realistic price process for evolving forward curves


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RWE Supply & Trading 7/20 /2014 PAGE 3

Gas Swing/Take-or-Pay Contracts

> Holder has rights to purchase gas each day subject to (e.g.)

Volume off-take limits daily, yearly and possibly sub-yearly

Contract price index to tradable or illiquid products, possibly withvolume dependent discounts

Inter-year constraints make-up, carry-forward

Sellers options to interrupt supply at short notice

Physical volume risks delivery shortfall, field depletion

> Historically, contracts have beenlong-term agreements linked to theoperational life of a gas field
http://www.google.com/imgres?imgurl=http://pubs.usgs.gov/bul/b2211/images/B2211Fig02_opt.gif&imgrefurl=http://pubs.usgs.gov/bul/b2211/b2211.html&usg=__RMSGcKNj8psTzMiHPnOc5Ly9tLs=&h=431&w=557&sz=23&hl=en&start=1&tbnid=VmSGvzCdJ1HGFM:&tbnh=103&tbnw=133&prev=/images%3Fq%3Dgas%2Bfield%2Bnorth%2Bsea%26um%3D1%26hl%3Den%26gbv%3D1%26tbs%3Disch:1&um=1&itbs=1http://www.google.com/imgres?imgurl=http://pubs.usgs.gov/bul/b2211/images/B2211Fig02_opt.gif&imgrefurl=http://pubs.usgs.gov/bul/b2211/b2211.html&usg=__RMSGcKNj8psTzMiHPnOc5Ly9tLs=&h=431&w=557&sz=23&hl=en&start=1&tbnid=VmSGvzCdJ1HGFM:&tbnh=103&tbnw=133&prev=/images%3Fq%3Dgas%2Bfield%2Bnorth%2Bsea%26um%3D1%26hl%3Den%26gbv%3D1%26tbs%3Disch:1&um=1&itbs=1http://www.google.com/imgres?imgurl=http://pubs.usgs.gov/bul/b2211/images/B2211Fig02_opt.gif&imgrefurl=http://pubs.usgs.gov/bul/b2211/b2211.html&usg=__RMSGcKNj8psTzMiHPnOc5Ly9tLs=&h=431&w=557&sz=23&hl=en&start=1&tbnid=VmSGvzCdJ1HGFM:&tbnh=103&tbnw=133&prev=/images%3Fq%3Dgas%2Bfield%2Bnorth%2Bsea%26um%3D1%26hl%3Den%26gbv%3D1%26tbs%3Disch:1&um=1&itbs=1


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Gas Storage

> Option to inject or withdraw specified volumes of gas each day:

Total volume in store must stay between min and max limits

Injection/withdrawal costs may be commodity price dependent

Injection/withdrawal rates may be dependent on volume in store

Number of injection-withdrawal cycles in the storage period maybe limited

> Storage agreement can relate tophysical facility or virtual contract


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Power Plant and Tolling Deals

> Options to dispatch a power plant buy fuel and carbon, sell power

> Dispatch decision changes plant operating regime and incurs fixed costs

Start-up and cycle costs may be commodity price dependent

> Dispatch decision taken frequently (daily half -hourly) but may need torespect plant engineering

Ramp rates, min on/off times, start warmth

> Plant operation may be subject to emission constraints

UK opted-out plant has unit sulphur and stack running hours limits

> Supply logistics mean fuel delivery to coal stations is not just -in- time

Port to station delivery constraints and coal stocking options
http://www.google.com/imgres?imgurl=http://www.utilityweek.co.uk/news/didcotMAIN.jpg&imgrefurl=http://www.utilityweek.co.uk/news/uk/electricity/siemens-wins-contract-to-refur.php&usg=__xenAuSvSkSp6enxW3SvJSrpOHMM=&h=305&w=458&sz=65&hl=en&start=14&tbnid=XeTx0XJ74nY9OM:&tbnh=85&tbnw=128&prev=/images%3Fq%3Ddidcot%2Bpower%2Bplant%26um%3D1%26hl%3Den%26sa%3DG%26gbv%3D1%26tbs%3Disch:1&um=1&itbs=1


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Energy Asset Options

ComplexPortfolio

ofOptions

TimeValue

How much in

theory?

How much can becaptured in the

real world?

Constrained Exercise

ContingentOptions

Need to optimiseexercise decisions

when valuing

Forward priceprocess isimportant


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Price Processes Governing Forward Curve Evolution

> Dynamics of curve movements

How different points along the curve can shift relative to each other

> Distribution of individual prices/returns

Presence of fat tails

> Mechanism by which successive prices/returns evolve

Existence of memory effects

> Cross Commodity relationships

Correlation/co-integration

Delivery Date


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Energy Assets in Traded Markets

Exposures tomultiple

commodities

Exercise (exposures)at granularities finerthan market trades

Deliveryvolumes

greater thanmarket trades

Exposuresbeyond

liquid tenors

Price risksarising fromvolume risks

How to build a realistic

price process?

How to hedge effectively with standard tradableproducts in the presence of real world market frictions?


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Energy Asset Valuation - Business Requirements

> Valuations of initial transactions e.g.

Acquisition of physical gas storage or power plant

Gas off-take and plant tolling contracts

Virtual deals and auction bids

> Daily reporting of P&L, position and risks

> Active management of assets

Exercise/hedging decision support tools for traders


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Intrinsic Valuation Models

> Optimise operation of asset against static forward curves

Typical methods are DP, LP and MIP

> Rich modelling of physical complexity

E.g. coal station with fuel logistics, plant dynamics and emission limits

> Capability to optimise portfolios containing long and short assets

E.g. swing and storage contracts with SOS constraint

> LP and MIP are easily extendable to accommodate non-standard features

> Models only provides intrinsic value and static position

But time value and delta may be estimated by rolling intrinsic simulations


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Stochastic Valuation Models> Optimise operation of asset to maximise expected value under an assumed

spot/forward price process

> Generally restricted to a single asset with limited physical features

> Standard approach is SDP on a trinomial forest

Limited to single factor price process and no more than 2/3 commodities

Typically minutes to value storage with level dependent rates, but hours ifa cycle constraint is added

> Least Squares Monte Carlo is slower but can accommodate any multi-factorprice process and many commodities

E.g. gas swing with contract price indexed to a basket of oil products

> Models determine time value and delta

But the validity of this time value needs to be understood and addressed


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Time Value in the Real World

> The key question is how much time value can be captured by operating anasset and hedging exposures in underlying commodity markets

And what value is at risk

> The classic stochastic models do not fully address this question because

They make assumptions about price processes that may be wrong

Price process parameters cannot even be observed (how to calibrate)

No account is taken of the risks and costs of real-world market frictions

Standard products, clip sizes, volume limits, depth dependent bid-offer

> Crucially, the concept of a universal fair time value does not really exist

It depends on the risk preferences of the counterparties


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Valuation against an Optimal Hedge Strategy

> The value we extract from an asset depends on how we operate and hedge it:

The model and parameters we use to determine exercise and exposure

Our hedging strategy frequency and how we optimise the trade-offbetween hedge costs and risks in the presence of market frictions

> We can execute this process against an evolving forward curve scenario at

each market trading date we take the prevailing forward curve and

Run a chosen model to optimise the asset and determine exposures

Put incremental hedges in place in line with our hedging strategy

> We keep track of the asset and hedge P&L to determine the value capturedfrom the asset under the evolving curve scenario

> We are free to optimise the asset against a fine granularity forward curve butcan only hedge at standard product granularity and must pay bid-offer


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Storage Value CaptureStorage and Hedge P&L without Transaction Costs

-10

-5

0

5

10

15

20

25

30

Time

M t M

Storage Hedge Realised Total

Total Storage and Hedge P&L

0

2

4

6

8

10

12

14

16

18

Time

M t M

Without Transaction Costs With Transaction Costs

> 1 year storage

> LSMC hedge model

> Historic back test

> Initial valuation and hedgeplaced 1 week before start ofstorage period

> Hedge costs not insignificant

> P&L without transactioncosts relatively flat


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Generation and Use of Evolving Curve Scenarios

> Back tests against historic forward curves

Select best model (rolling intrinsic or rolling stochastic), model parametersand hedging strategy

Sense check verification of valuation results

> Multiple simulations of curve evolution from a model Distribution of value captured

Reserve for hedge effectiveness and value adjustment for model

> Stress tests built by mapping historic returns onto current forward curve

Verification of value distribution and reserve for model risk

> Valuations can be obtained with and without transaction costs


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Valuation Infrastructure> The above valuation methodology does not replace classic valuation models

but executes them many times at the heart of a simulated hedging strategy

> A flexible IT framework is required that allows analysts to construct andevaluate hedging strategies from pluggable components

Valuation models from pricing libraries

Standard product trade generators and pricers

Hedge cost minimisation algorithms

Forward curve scenario generators

> P&L calculations can be taken care of by the core framework

> Valuations can be computationally intensive, but can be distributed acrossmultiple cores of servers and desk top PCs


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Modelling Forward Curve Evolution

> Curves start at next trading day

> As curve evolves delivery dates roll to

maturity Tenor of fixed delivery reduces

> But volatility of non-storable commoditiestends to increase with tenor

Volatility Term Structure

0%

20%

40%

60%

80%

100%

120%

140%

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Tenor (y)


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Model Calibration using Historic Price Returns> Isolate volatility term effects by calibrating against fixed-tenor price returns

De-seasonalise prices or bucket fixed-delivery returns onto fixed tenor

> Use daily contract returns for a few prompt days then month contract returns

> HJM-style model may be built by using PCA to map onto stochastic factors

where the dz k( ) are i.i.d. normal variates

> But time series of fixed tenor returns do not really support such a model

Strong linear and non-linear auto-correlations with volatility clustering;non-Gaussian distributions, particularly fat tails; complex spot/forwardprice dynamics

tT,tdzT,tFT,tdF

r K

1k k k


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OGARCH Curve Model

Multi-VariateReturn Time

Series

UncorrelatedComponent

Series

IndependentComponent

Series

ConditionalMean andVolatility

Equations

ICA

ARMA, GARCH, OLS,Max Likelihood,

Stability Constraints

ResidualDistribution

(Normal,Student t, NIG)

PCA DimensionReduction

Sample residual distributions, inverttransformations, apply simulated returns toevolve curve and roll to maturity

Integratespot model

?


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Dimension Reduction for Gas Curve Model

> PCA reproduces volatility betterthan correlation and only achieves

linear independence

> ICA components satisfy a strongerform of independence but are moredifficult to model

Correlation with M+18 - 4 Factor Model (Volatility Understated by 2%)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 0.5 1 1.5 2 2.5

Tenor (y)

Hist

PCA

Correlation with M+18 - 8 Factor Model (Volatility Understated by 1%)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 0.5 1 1.5 2 2.5

Tenor (y)

Hist

PCA

Average Correlation between Component Returns^N

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5

N

PCA

ICA


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ARMA/GARCH: Auto-Correlation and Distribution Capture

> ARMA/GARCH can reduce auto-correlation in returns and their

squares

> ARMA/GARCH with a NIG residualdistribution can replicate fat tails toa large extent

Auto-Correlation of Samples

-1%

1%

3%

5%

7%

9%

11%

1 2 3 4

Component

Historic Returns

Model Residuals

Auto-Correlation of Samples^2

-3%

2%

7%

12%

17%

22%

1 2 3 4

Component

Historic Returns

Model Residuals

Kurtosis

0

2

4

6

8

10

12

14

1 2 3 4

Component

Historic

Model


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Modelling Multi-Commodity Curve Evolution

> OGARCH can be applied to model evolution of multiple commodity curves

> But a pure-returns based model only sees short-term curve dynamics andcannot capture long-term association between commodity prices

Unrealistic commodity spreads can develop, whereas in reality macro-economic and infrastructure relationships would tend to prevent this

> An alternative is the Vector Error Correction Model (VECM):

> Here X t is a vector of fixed-tenor log prices at time t, k contain ARcoefficients, and captures long-run, co-integrated relationships

> The model can be calibrated using Johansen method to establish stationarycombinations of prices, OLS to fit coefficients, and maximum likelihood todetermine a distribution to simulate the stochastic residual in t

1-tttttK t

1-K

1k k tk t XXX,XXX


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OGARCH vs VECM for Oil Time SpreadOGARCH

- 3 6 . 5 - 3

3 - 2

9 . 5 - 2 6

- 2 2 . 5 - 1

9 - 1

5 . 5 - 1 2

- 8 . 5 - 5

- 1 . 5 2 5 .

5 9 1 2

. 5 1 6 1 9

. 5 2 3 2 6

. 5 3 0 3 3

. 5 3 7

VECM

- 3 6 . 5 - 3

3 - 2

9 . 5 - 2 6

- 2 2 . 5 - 1

9 - 1

5 . 5 - 1 2

- 8 . 5 - 5

- 1 . 5 2 5 .

5 9 1 2

. 5 1 6 1 9

. 5 2 3 2 6

. 5 3 0 3 3

. 5 3 7

Spread Distributions

History

Simulated


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Demonstrating Validity of Price Process Models

> Calibration goodness of fit measures

> Animations of forward curve evolution

> Price and return distributions for commodity legs and spreads

Including time spreads

> Moment analysis

> Skill scores

> Managing and explaining extreme price behaviour

Many challenging problems still to be overcome!

john putney

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