Proc IWIF-II, 2007, Chengdu 1 Model of Financial Market : Insights and its Possible Application C. H. Yeung 1, K. Y. Michael.

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


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) ?


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 ?


1. What modifications are we making?


The ModelIndividual actions

Collective actions

Pricechanges

N agents Each agent makes decision from his/her

best strategy (higher virtual payoff)


The Strategy +1/ -1/ 0, buy/ sell/ hold

decisions (different from MG)

Max. Allowed Position K


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


2. What important aspects

of real markets should be added

to capture basic features?

(1) Price sensitivity &

(2) Market impact


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


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 !!


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 !!


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 !!


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 ???


Phase Diagram of Final State

Arbitrageurs phase ??

Trendsetter phase ??

Irregular phase ??

Mixture phase ??


Arbitrageurs phase

For β ≤ 0.5 ⇒Period-2 cycle for P(t) !?

)1()()1()(:Impact Market T tPtPtP

Buy!

sell!

Gain!!Too unrealistic!!


Trendsetter state

Arbitrageur state

VS

Periodic with characteristic pattern

Period much longer than period 2 !!

What arethey doing?


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 !!!


)1()()1()(:Impact Market


T

tPtPtP

tAtAtPtP

Period 2Unrealistic!

Too periodic!

orUnrealistic!


What’s the interpretations?The real market is possibly……

Positive

Negative

)1()()1()(:Impact Market


T

tPtPtP

tAtAtPtP

Possible parameters of real market !!

Agent’s wealth


3. Negative sum? Positive sum?

Zero sum?


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 ?


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)


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%


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%


Lo

ss p

er s

tep

Positive gain for Investors andMarket maker !!~> Participation incentives


4. Can we apply these financial models on real financial data ?


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)


Results (HSI from 1987 – 2007)

HSIx 7.5 times

Best 3 among10000 Agentsx 17 times

5 randomagents


Initially, w(1987)/P(1987) = 5

Wealth growsfaster than inflation

Wealth growsslower than inflation


Comparison with other models- % of gaining agents

≈ 11% of agents in this model Beat HSI inflation in this 20 years


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 !


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


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


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


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

Proc IWIF-II, 2007, Chengdu 1 Model of Financial Market : Insights and its Possible Application C. H. Yeung 1, K. Y. Michael.

Documents

market impact slide

chengdu market impact

chengdu price movement

real price

chengdu wealth

chengdu positivesum

chengdu period

agents wealth slide