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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

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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 ?

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

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

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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?

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

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

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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?

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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

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The Minority Game (MG) 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 Why Do Stylized Facts Occur? +1 WIN WIN ……

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Adaptive Learning in MG Some Definitions The th agents bid The total bid (excess demand) Score all the strategies The Adaptive Learning of Agents What Do Stylized Facts Occur? Only those being minority get positive pay-offs

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

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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

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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

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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

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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 Why Do Stylized Facts Occur?

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

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Thresholds Effect on Fat-Tailed Distribution Without the 0-Strategy With the 0-Strategy Why Do Stylized Facts Occur?

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

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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?

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

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The Profitable Chances Production Consumption S1: Chance Rich VC Disappeared S2: Chance Critical VC Emerged S3: Chance Depleted VC Disappeared Three Scenarios in the Modeled Market

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Evidence 1 and 2 The increase of producer increases the predictability The increase of speculator decreases the predictability Why Do Stylized Facts Occur?

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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. Evidence 3 and 4

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

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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?

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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 How to Utilize Stylized Facts? The Predictability of Time Series: GCMG market model; FX Market (only sign); and a spin model on network for stock market

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

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A Simple Preliminary Test To Predict Another MG Comparison with the Prediction of a Random Walk How to Utilize Stylized Facts?

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

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The Reason for the failure How to Utilize Stylized Facts? The Price-Change DistributionAutocorrelation of Volatility

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How to Utilize Stylized Facts? Prediction of the FX Market

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