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Market Mechanism Analysis Using Minority Game Market Models

Market Mechanism Analysis Using Minority Game Market Models. Y. Chen, T . Kohashi, M. Komiya, Y. Hashimoto and H. Ohashi Department of Quantum Engineering and Systems Science Graduate School of Engineering, The University of Tokyo. Contents of the Presentation.

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Market Mechanism Analysis Using Minority Game Market Models

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  1. Market Mechanism Analysis Using Minority Game Market Models Y. Chen, T. Kohashi, M. Komiya, Y. Hashimoto and H. Ohashi Department of Quantum Engineering and Systems Science Graduate School of Engineering, The University of Tokyo

  2. Contents of the Presentation Concerning the Price Fluctuation of Financial Assets What are “stylized facts” ? Why do “stylized facts” occur ? How to utilize “stylized facts” ?

  3. What to Observe in the Market? • The Asset Price • The Price-Changes • Return • Log Return Nikkei 225 index from 1970 to 2002. Nikkei 225 consists of the 225 top-rated, blue-chip Japanese companies listed in the First Section of the Tokyo Stock Exchange. What Are Stylized Facts?

  4. Stylized Facts Observed • The Fat-Tailed Price Distribution • The Volatility Clustering Calculated from the minute data of Yen-Dollar rate, 2006.8-2007.1. What Are Stylized Facts?

  5. The Classic Theory for Financial Markets • The Efficient Market Hypothesis (EMH)All information concerning a financial asset is already incorporated into the current price. • The Implications • No way to make risk-free profit • Completely rational traders • Random-walk like price-changes • Independent Price-Changes • Identical PDFs • Gaussian PDF for Price-Changes What Are Stylized Facts?

  6. The Fat-Tailed Distribution • The Extraordinarily High Risk • The Universal Existence • The Power-Law Distribution Levy Distribution The Six Sigma Probability From Gopikrishna et al.C What Are Stylized Facts?

  7. The Volatility Clustering • Exponential Decay of the Autocorrelation • The Problem of EMH • A Universal Existence From Gopikrishna et al.C What Are Stylized Facts?

  8. Available Approaches to Analyze the Market • Standard Finance Theory • The Stochastic Differential Equation • Limitations • Based on wrong assumptions • Awkward to describe traders’ behaviors • Econophysics • Concepts and Theories • Phase transition • Chaos, fractal • Self-organization • Approaches • Replica method • Normalization group method • Agent-based simulations • Evolutionary computations Why Do Stylized Facts Occur?

  9. Simple Agent Model for Complex Price Dynamics • Simplified Description of Traders’ Activities • No way to model even one trader perfectly • Easier to analyze the market mechanism • Collective Fluctuation Recovered to that of Price-Changes • The large scale collective dynamics is often insensitive to small scale behaviors • Succeeded Examples in Physics • Spin model for phase transition • Percolation model for critical phenomena • Lattice gas model for fluid flow Why Do Stylized Facts Occur

  10. The Minority Game (MG) +1 +1 -1 • A Multi-Agent, Multi-Strategy, Repeated Game • Those Belonging to the Minority Win the Game • Parameters to Specify a Minority Game • Player number • Number of strategies for each player • Memory of the player WIN +1 +1 +1 -1 WIN …… Why Do Stylized Facts Occur?

  11. Adaptive Learning in MG • Some Definitions • Theth agent’s bid • The total bid (excess demand) • Score all the strategies • The Adaptive Learning of Agents Only those being minority get positive pay-offs What Do Stylized Facts Occur?

  12. Characteristics of MG • Basic Properties • Volatility • Predictability • Congestion in strategy space • Emergence of Cooperation • Symmetric to Asymmetric Phase Transition Why Do Stylized Facts Occur?

  13. Relation between MG and Market Model 1 • Time Evolution of an Idealized Market Model • Traders’ actions: strategic investment; position clearing; evaluation of strategies • Asset price / Traders’ capital • Scores of investment strategies

  14. Relation between MG and Market Model 2 • Details of the Model • Traders’ order • Clear positions • Price formation • Demand and supply • Balance (D = S*p) • Score the strategies • Capital updates • Score updates

  15. Relation between MG and Market Model 3 • Simplification of the Model • Synchronization of traders • Neglect position-clearing and capital updates • Understanding the MG Market Model • Predict the future excess demand • Fundamentalists’ viewpoint • Chartists’ viewpoint

  16. Extension of the MG Market Model • Two Kinds of Traders: Producers and Speculators • Speculators have the right not to trade: GCMG • Definitions • Producer • Speculator • The 0-Strategy • Public Information • Threshold for Trade • Log-Return • Trade Volume • Scoring of the Strategies 0 +1 -1 +1 +1 0 -1 Why Do Stylized Facts Occur?

  17. Recovery of Stylized Facts • Fat Tailed Distribution • Volatility Clustering Why Do Stylized Facts Occur?

  18. Threshold’s Effect on Fat-Tailed Distribution • Without the 0-Strategy • With the 0-Strategy Why Do Stylized Facts Occur?

  19. The Effect of Speculation on Fat-Tailed Distribution • Speculation causes larger fluctuations • A phase transition with the increase of speculators Where the -3 power law emerges Why Do Stylized Facts Occur?

  20. Market Mechanism for Fat-Tailed Distribution • The Important Role of Threshold • In Model: the right not to play • In Real World: the Watch-And-Wait behavior of traders for various reasons • Other examples: Sand-Pile in SOC, Latent Heat …. • The Congestion in the Strategy Space • In Model: the self-incurred phase transition caused by the similarity of agents’ strategies and the optimization of the strategies through the adaptive learning • In Real World: Traders often have similar strategies or they learn the similar strategies Why Do Stylized Facts Occur?

  21. The Effect of Np/Ns on VC • Autocorrelation of the Volatility • The Correlation Time of Volatility Why Do Stylized Facts Occur?

  22. Three Scenarios in the Modeled Market e1 Production e2 The Profitable Chances e5 e3 e4 Consumption S1: Chance Rich VC Disappeared S2: Chance Critical VC Emerged S3: Chance Depleted VC Disappeared Why Do Stylized Facts Occur?

  23. Evidence 1 and 2 • The increase of producer increases the predictability • The increase of speculator decreases the predictability e1 e2 Why Do Stylized Facts Occur?

  24. Evidence 3 and 4 e3 e4 When the number of speculator is (relatively) too small, the predictability becomes high while the correlation low When the number of speculator is (relatively) too large, the predictability is zero while the correlation decreases. Why Do Stylized Facts Occur?

  25. Evidence 5 e5 Correlation time reaches its maximum right after the predictability is depleted Why Do Stylized Facts Occur?

  26. Market Mechanism for Volatility Clustering • The Interaction between Different Types of Agents • In Model: Producers generates the predictability (profitable chance); Speculators competitively consume it • In Real World • Producers: Irrational Traders; Speculators: Rational Traders • The intelligent takes advantage of the others in financial market • The Criticality of Phase Transition in Information Space • In Model: The maximum of time correlation emerges when the predictability is just depleted • In Real World: The market always seems like efficient Why Do Stylized Facts Occur?

  27. Application of the Minority Game to Predicting Price • The Goal: To predict price-changes in financial markets • Is It Predictable? • Volatility clustering • The predictability • Why Use Minority Game • The simple, built-in adaptive learning • GA-like algorithm easily applicable The Predictability of Time Series: GCMG market model; FX Market (only sign); and a spin model on network for stock market How to Utilize Stylized Facts?

  28. The Modified Adaptive Learning Data Generation Another MG simulation A random walk A GCMG Simulation A Network Stock Market Model Simulation FX Data (2006.8-2007.1) The Predicting Method Financial Market Black Box complex mechanism Generate Learning Predict Predictor MG Minority Game optimization of strategy distribution How to Utilize Stylized Facts?

  29. A Simple Preliminary Test • To Predict Another MG • Comparison with the Prediction of aRandom Walk How to Utilize Stylized Facts?

  30. Two Further Tests • To predict the time series generated by aGCMG • To predict the time series generated by a network stock market model How to Utilize Stylized Facts?

  31. The Reason for the failure The Price-Change Distribution Autocorrelation of Volatility How to Utilize Stylized Facts?

  32. Prediction of the FX Market How to Utilize Stylized Facts?

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