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Model of Financial Market : Insights and its Possible Application

IWIF-II. Model of Financial Market : Insights and its Possible Application. C. H. Yeung 1 , K. Y. Michael Wong 1 . Y. C. Zhang 1,2. 1 Department of Physics, the Hong Kong University of Science and Technology, Hong Kong, China

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Model of Financial Market : Insights and its Possible Application

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  1. IWIF-II 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, China 2Institut de Physique Théorique, Université de Fribourg, 1700 Fribourg, Switzerland www.swingtum.com/institute/IWIF

  2. 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

  3. 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

  4. To include more realistic aspects … • What modifications are we making? • What important aspects of real markets should be added to capture basic features? • Negative sum? Positive sum? Zero sum? • Can we apply these financial models on real financial data ? www.swingtum.com/institute/IWIF

  5. 1. What modificationsare we making? www.swingtum.com/institute/IWIF

  6. Individual actions Price changes Collective actions The Model • N agents • Each agent makes decision from his/her best strategy (higher virtual payoff) www.swingtum.com/institute/IWIF

  7. The Strategy • +1/ -1/ 0, buy/ sell/ hold decisions (different from MG) • Max. Allowed PositionK www.swingtum.com/institute/IWIF

  8. Remark : For MG, Wealth = Cash + Stock Values in hand No. of stock in hand, Position www.swingtum.com/institute/IWIF

  9. 2. Whatimportant aspects of real markets should be added to capture basic features? (1) Price sensitivity & (2) Market impact www.swingtum.com/institute/IWIF

  10. Price rises!! Collective Actions What are price sensitivity and market impact? • Price Sensitivity • Sensitivity of stock price on agent’s collective actions • Define γ : Individual Actions Price movement = (Collective actions)γ www.swingtum.com/institute/IWIF

  11. Market Impact !! Synchronized Actions !! • Market Impact • The impact of synchronized decisions from peer investors during transaction • Define β Transaction price = Current price +β(Synchronized price movement) www.swingtum.com/institute/IWIF

  12. (1) Price sensitivity γ Price movement = (Collective actions)γ (2) Market Impact β Transaction price = Current price +β(Synchronized price movement) These 2 aspects we would like to put in the model !! www.swingtum.com/institute/IWIF

  13. Collective actions !! Price Sensitivity!! Market Impact !! • Decision of agent ai(t) = +1, 0, -1 • Real Price: • Transaction Price PT(t) = Price in between P(t+1) and P(t) www.swingtum.com/institute/IWIF

  14. Negative Positive Results Final State of the system Agents’ Wealth www.swingtum.com/institute/IWIF 3 phases have positive wealth ???

  15. Irregular phase ?? Trendsetter phase ?? Phase Diagram of Final State Mixture phase ?? Arbitrageurs phase ?? www.swingtum.com/institute/IWIF

  16. sell! Buy! For β≤ 0.5⇒ Period-2 cycle for P(t) !? Arbitrageurs phase Gain!! Too unrealistic!! www.swingtum.com/institute/IWIF

  17. Trendsetter state What are they doing? • Periodic with characteristic pattern • Period much longer than period 2 !! VS Arbitrageur state www.swingtum.com/institute/IWIF

  18. Trend setters (winners) Trend followers (winners) Late followers (losers) Start to sell !! (Set up the downward trend) Follow the trend !! I was late... Trendsetter state Depend on strategies, 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

  19. Too periodic! Period 2 Unrealistic! or Unrealistic! www.swingtum.com/institute/IWIF

  20. Negative Positive What’s the interpretations?The real market is possibly…… Agent’s wealth www.swingtum.com/institute/IWIF Possible parameters of real market !!

  21. 3.Negative sum? Positive sum? Zero sum? www.swingtum.com/institute/IWIF

  22. 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 www.swingtum.com/institute/IWIF Market Maker ?

  23. 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

  24. Transaction Cost (% of P(t))+ Evolution Positive gain for Investors and Market maker !! ~> Participation incentives www.swingtum.com/institute/IWIF

  25. 4. Can we apply these financial models onreal financial data ? www.swingtum.com/institute/IWIF

  26. 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

  27. Results (HSI from 1987 – 2007) Best 3 among 10000 Agents x 17 times HSI x 7.5 times 5 random agents www.swingtum.com/institute/IWIF

  28. Initially, w(1987)/P(1987) = 5 Wealth grows slower than inflation Wealth grows faster than inflation www.swingtum.com/institute/IWIF

  29. 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

  30. Wealth Game Minority Game • Wealth Game has the largest % of gaining agents • But for the best investor……. x 25 times x 17 times x 7.5 times x 7.5 times Minority Game has more outstanding best investor ! www.swingtum.com/institute/IWIF

  31. Difference in wealth counting….. Wealth Game Minority Game VS with Trend following? • Positive sign VS negative sign • Position dependence VS Single bid • dependence • 3.Small time lag Longer memory www.swingtum.com/institute/IWIF

  32. Wealth Game Vs Minority Game Another similar test : Wealth independent Max Pos. with w(0) = 0 Best investors are not as rich as MG, but most are gaining Best investors are more outstanding Most agents are losing www.swingtum.com/institute/IWIF

  33. 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 HSI Wealth Game: better average performance Minority game: more outstanding best agents www.swingtum.com/institute/IWIF

  34. 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 www.swingtum.com/institute/IWIF

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