proc iwif-ii, 2007, chengdu 1 model of financial market : insights and its possible application c....
TRANSCRIPT
Proc IWIF-II, 2007, Chengdu
www.swingtum.com/institute/IWIF 1
Model of Financial Market :Insights and its Possible Application
C. H. Yeung1, K. Y. Michael Wong1. Y. C. Zhang1,2
1Department of Physics, the Hong Kong University of Science and Technology, Hong Kong, China2Institut de Physique Théorique, Université de
Fribourg, 1700 Fribourg, Switzerland
IWIF-II
www.swingtum.com/institute/IWIF 2Proc IWIF-II, 2007, Chengdu
Outline Introduction
Our model (Wealth Game) VS Minority Game ?
Price Sensitivity and Market Impact – Phase Diagram of final states and wealth
Market Makers, Transaction Cost and Evolutions – Positive gain for agents and market makers
Application on real data: Trading with Hang Seng Index
Conclusion
www.swingtum.com/institute/IWIF 3Proc IWIF-II, 2007, Chengdu
Introduction Minority Game (MG) – The model by D.
Challet and Y. C. Zhang in 1997 Successful and simple model of Financial
Market which states that the minority choices will win
One of the main concern for investors:
negative-sum (MG)
VS
positive-sum (Real market) ?
www.swingtum.com/institute/IWIF 4Proc IWIF-II, 2007, Chengdu
To include more realistic aspects …
1. What modifications are we making?
2. What important aspects of real markets should be added to capture basic features?
3. Negative sum? Positive sum? Zero sum?
4. Can we apply these financial models on real financial data ?
www.swingtum.com/institute/IWIF 5Proc IWIF-II, 2007, Chengdu
1. What modifications are we making?
www.swingtum.com/institute/IWIF 6Proc IWIF-II, 2007, Chengdu
The ModelIndividual actions
Collective actions
Pricechanges
N agents Each agent makes decision from his/her
best strategy (higher virtual payoff)
www.swingtum.com/institute/IWIF 7Proc IWIF-II, 2007, Chengdu
The Strategy +1/ -1/ 0, buy/ sell/ hold
decisions (different from MG)
Max. Allowed Position K
www.swingtum.com/institute/IWIF 8Proc IWIF-II, 2007, Chengdu
Wealth = Cash + Stock Values in hand
)]()1()[1( changeWealth TT tPtPtki
No. of stock in hand,Position
1
0'
)'()1(t
tii tatk
Remark :For MG,
jji
i
tata
tAta
)()(
)()(
changeWealth
www.swingtum.com/institute/IWIF 9Proc IWIF-II, 2007, Chengdu
2. What important aspects
of real markets should be added
to capture basic features?
(1) Price sensitivity &
(2) Market impact
www.swingtum.com/institute/IWIF 10Proc IWIF-II, 2007, Chengdu
What are price sensitivity and market impact? Price Sensitivity- Sensitivity of
stock price on agent’s collective actions
Define γ : Individual Actions
Pricerises!!
Price movement = (Collective actions)γ
CollectiveActions
www.swingtum.com/institute/IWIF 11Proc IWIF-II, 2007, Chengdu
Market Impact - The impact of
synchronized decisions from peer investors during transaction
Define β
Transaction price = Current price
+ β (Synchronized price movement)
MarketImpact !!
Synchronized Actions !!
www.swingtum.com/institute/IWIF 12Proc IWIF-II, 2007, Chengdu
Price movement = (Collective actions)γ
(1) Price sensitivity γ
Transaction price = Current price
+ β (Synchronized price movement)
(2) Market Impact β
These 2 aspects we would like to put in the model !!
www.swingtum.com/institute/IWIF 13Proc IWIF-II, 2007, Chengdu
Decision of agent ai(t) = +1, 0, -1
Real Price:
Transaction Price PT(t) = Price in between P(t+1) and P(t)
|)(|)]([sign)()1( tAtAtPtP
N
ii tatA
1
)()(
)()]([sign)(
)1()()1()(T
tAtAtP
tPtPtP
Collective actions !!
PriceSensitivity!!
Market Impact !!
www.swingtum.com/institute/IWIF 14Proc IWIF-II, 2007, Chengdu
Positive
Negative
Results )1()()1()(:Impact Market
|)(|)]([sign)()1( :Sensivity Price
T
tPtPtP
tAtAtPtP
Final State of the system
Agents’ Wealth
3 phases have positive wealth ???
www.swingtum.com/institute/IWIF 15Proc IWIF-II, 2007, Chengdu
Phase Diagram of Final State
Arbitrageurs phase ??
Trendsetter phase ??
Irregular phase ??
Mixture phase ??
www.swingtum.com/institute/IWIF 16Proc IWIF-II, 2007, Chengdu
Arbitrageurs phase
For β ≤ 0.5 ⇒Period-2 cycle for P(t) !?
)1()()1()(:Impact Market T tPtPtP
Buy!
sell!
Gain!!Too unrealistic!!
www.swingtum.com/institute/IWIF 17Proc IWIF-II, 2007, Chengdu
Trendsetter state
Arbitrageur state
VS
Periodic with characteristic pattern
Period much longer than period 2 !!
What arethey doing?
www.swingtum.com/institute/IWIF 18Proc IWIF-II, 2007, Chengdu
Trendsetter state
Start to sell !!(Set up the
downward trend)
Follow the trend !! I was
late...
Trend setters (winners)Trend followers (winners)Late followers(losers)
Depend onstrategies, eg:↑↑↓ buy/sell/hold↑↓↓ buy/sell/hold….
We didn’t teach them to set up and follow trend !!But they do it !!!
www.swingtum.com/institute/IWIF 19Proc IWIF-II, 2007, Chengdu
)1()()1()(:Impact Market
|)(|)]([sign)()1( :Sensivity Price
T
tPtPtP
tAtAtPtP
Period 2Unrealistic!
Too periodic!
orUnrealistic!
www.swingtum.com/institute/IWIF 20Proc IWIF-II, 2007, Chengdu
What’s the interpretations?The real market is possibly……
Positive
Negative
)1()()1()(:Impact Market
|)(|)]([sign)()1( :Sensivity Price
T
tPtPtP
tAtAtPtP
Possible parameters of real market !!
Agent’s wealth
www.swingtum.com/institute/IWIF 21Proc IWIF-II, 2007, Chengdu
3. Negative sum? Positive sum?
Zero sum?
www.swingtum.com/institute/IWIF 22Proc IWIF-II, 2007, Chengdu
Positive-sum?Where does the money come
from? Note: Supply and Demand is not balanced in this
model There is a Market Maker behind the game Market Maker is clearing the extra supply and
demand (doing opposite as the actual agents do) So, agents gain,
Market Maker loses All together ~> zero sum
Market Maker ?
www.swingtum.com/institute/IWIF 23Proc IWIF-II, 2007, Chengdu
No Market Maker, supply and demand have to be balanced
~> when one agent is holding a buying position, someone else must be holding a selling position
~> zero-sum for agents
Can both Agents and Market Maker gain? Transaction cost + evolution of agents
(agents losing money are leaving the market)
www.swingtum.com/institute/IWIF 24Proc IWIF-II, 2007, Chengdu
Transaction Cost (% of P(t))+ EvolutionMarket Maker's Gain VS Transaction Cost
-100
-50
0
50
100
150
0.00% 0.02% 0.04% 0.06% 0.08% 0.10%
Transaction Cost (% of Price)
G
ain
per
ste
p
Existing Agent's Gain VS Transaction Cost
0
2000
4000
6000
8000
10000
12000
0.00% 0.02% 0.04% 0.06% 0.08% 0.10%
Transaction Cost (% of Price)
Gai
n
Withdrawing Agent's Loss VS Transaction Cost
-140
-120
-100
-80
-60
-40
-20
0
0.00% 0.02% 0.04% 0.06% 0.08% 0.10%
Transaction Cost (% of Price)
Lo
ss p
er s
tep
Positive gain for Investors andMarket maker !!~> Participation incentives
www.swingtum.com/institute/IWIF 25Proc IWIF-II, 2007, Chengdu
4. Can we apply these financial models on real financial data ?
www.swingtum.com/institute/IWIF 26Proc IWIF-II, 2007, Chengdu
Application on real data:Hang Seng Index (HSI)
To convince ourselves that the model share similarities with real market, we test the applicability of the model on HSI
Real HSI as external signals, stock price in the model
Agents are given a certain amount of initial wealth, for initial investment
Wealth dependence maximum position K(t) = Wealth(t) / Price(t)
www.swingtum.com/institute/IWIF 27Proc IWIF-II, 2007, Chengdu
Results (HSI from 1987 – 2007)
HSIx 7.5 times
Best 3 among10000 Agentsx 17 times
5 randomagents
www.swingtum.com/institute/IWIF 28Proc IWIF-II, 2007, Chengdu
Initially, w(1987)/P(1987) = 5
Wealth growsfaster than inflation
Wealth growsslower than inflation
www.swingtum.com/institute/IWIF 29Proc IWIF-II, 2007, Chengdu
Comparison with other models- % of gaining agents
≈ 11% of agents in this model Beat HSI inflation in this 20 years
www.swingtum.com/institute/IWIF 30Proc IWIF-II, 2007, Chengdu
Wealth Game has the largest % of gaining agents
But for the best investor…….
Wealth Game Minority Game
x 7.5 times
x 17 times x 25 times
x 7.5 times
Minority Game has more outstanding best investor !
www.swingtum.com/institute/IWIF 31Proc IWIF-II, 2007, Chengdu
Difference in wealth counting…..
1
0'
)'()1(t
tii tatk
Wealth Game Minority Game
VSwith
)]()1()[(
changeWealth
HSIHSI tPtPtai )]()1()[1(
changeWealth
HSIHSI tPtPtki
1.Positive sign VS negative sign2.Position dependence VS Single bid
dependence3.Small time lag
Trend following?
Longer memory
www.swingtum.com/institute/IWIF 32Proc IWIF-II, 2007, Chengdu
Wealth Game Vs Minority Game
Another similar test :Wealth independent Max Pos. with w(0) = 0
Best investors are more outstanding
Most agentsare losing
Best investors are not as rich as MG, but most aregaining
www.swingtum.com/institute/IWIF 33Proc IWIF-II, 2007, Chengdu
Conclusion Behaviors resembling real investors emerge
naturally form this simple model Possible values of γ and β (price sensitivity
and market impact) in real market can be conjectured form the phase diagrams (irregular phase with positive wealth)
Wide participation incentives: positive sum for both existing agents and market maker
The model is tested by using real HSIWealth Game: better average performanceMinority game: more outstanding best agents
www.swingtum.com/institute/IWIF 34Proc IWIF-II, 2007, Chengdu
Thank You!!
Questions & Answers Session
Acknowledgement: Supported by the Research Grant Council of Hong Kong(DAG05/06.SC36 and HKUST603606)"
All cartoon figures from coolclip.com