A minimal noise trader model with realistic time series

Simulations of agent-based models have shown that the stylized facts (unit-root, fat tails and volatility clustering) of financial markets have a possible explanation in the interactions among agents. However, the complexity, originating from the presence of non-linearity and interactions, often limits the analytical approach to the dynamics of these models. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing realistic statistical properties of returns, in close quantitative accordance with the empirical analysis. The simplicity of the system also permits some analytical insights using concepts from statistical mechanics and physics. In our model, the traders are divided into two groups : fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by Kirman [22]. The statistical analysis of our simulated data shows long-term dependence in the auto-correlations of squared and absolute returns and hyperbolic decay in the tail of the distribution of the raw returns, both with estimated decay parameters in the same range like empirical data. Theoretical analysis, however, excludes the possibility of ’true’ scaling behavior because of the Markovian nature of the underlying process and the finite set of possible realized returns. The model, therefore, only mimics power law behavior. Similarly as with the phenomenological volatility models analyzed in LeBaron [25], the usual statistical tests are not able to distinguish between true or pseudo-scaling laws in the dynamics of our artificial market.

[1]  Richard H. Day,et al.  Bulls, bears and market sheep , 1990 .

[2]  Shu-Heng Chen,et al.  On the emergent properties of artificial stock markets: the efficient market hypothesis and the rational expectations hypothesis , 2002 .

[3]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  M. Marsili,et al.  From Minority Games to real markets , 2000, cond-mat/0011042.

[5]  B. Mandelbrot.  Stochastic volatility, power laws and long memory , 2001 .

[6]  Jasmina Arifovic,et al.  Statistical properties of genetic learning in a model of exchange rate , 2000 .

[7]  Koichi Hamada,et al.  Statistical properties of deterministic threshold elements - the case of market price , 1992 .

[8]  Andrea Gaunersdorfer,et al.  A Nonlinear Structural Model for Volatility Clustering , 2000 .

[9]  F. Diebold,et al.  Long Memory and Regime Switching , 2000 .

[10]  Alan Kirman,et al.  Ants, Rationality, and Recruitment , 1993 .

[11]  J. Farmer,et al.  The price dynamics of common trading strategies , 2000, cond-mat/0012419.

[12]  V. Eguíluz,et al.  Transmission of information and herd Behavior: an application to financial markets. , 1999, Physical review letters.

[13]  Kenneth A. Froot,et al.  The Dollar as an Irrational Speculative Bubble: a Tale of Fundamentalisists , 1986 .

[14]  A simple linear time series model with misleading nonlinear properties , 1999 .

[15]  M. Ausloos,et al.  Market Fluctuations I: Scaling, Multiscaling, and Their Possible Origins , 2002 .

[16]  M. Marchesi,et al.  VOLATILITY CLUSTERING IN FINANCIAL MARKETS: A MICROSIMULATION OF INTERACTING AGENTS , 2000 .

[17]  M. Paczuski,et al.  Price Variations in a Stock Market with Many Agents , 1997 .

[18]  Bernardo A. Huberman,et al.  Clustered volatility in multiagent dynamics , 1995, adap-org/9502006.

[19]  Thomas Lux,et al.  Genetic learning as an explanation of stylized facts of foreign exchange markets , 2003, 2003 IEEE International Conference on Computational Intelligence for Financial Engineering, 2003. Proceedings..

[20]  青木 正直,et al.  New approaches to macroeconomic modeling : evolutionary stochastic dynamics, multiple equilibria, and externalities as field effects , 1998 .

[21]  Blake LeBaron,et al.  Agent-based computational finance : Suggested readings and early research , 2000 .

[22]  R. Palmer,et al.  Artificial economic life: a simple model of a stockmarket , 1994 .

[23]  G. Iori.  A Microsimulation of Traders Activity in the Stock Market: The Role of Heterogeneity, Agents' Interactions and Trade Frictions , 2002 .

[24]  Florian Wagener,et al.  Bifurcation Routes to Volatility Clustering , 2000 .

[25]  Ignacio N. Lobato,et al.  Real and Spurious Long-Memory Properties of Stock-Market Data , 1996 .

[26]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[27]  Michele Marchesi,et al.  Testing for Non-Linear Structure in an Artificial Financial Market , 2001 .

[28]  S. Bornholdt,et al.  Expectation Bubbles in a Spin Model of Markets , 2001, cond-mat/0105224.

[29]  M. Goldman,et al.  On the Dynamic Behavior of Prices in Disequilibrium , 1980 .

[30]  B. M. Hill,et al.  A Simple General Approach to Inference About the Tail of a Distribution , 1975 .

[31]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[32]  Casper G. de Vries,et al.  Stylized Facts of Nominal Exchange Rate Returns , 1994 .

[33]  Timo Teräsvirta,et al.  A simple nonlinear time series model with misleading linear properties , 1999 .

[34]  Jeffrey A. Frankel,et al.  The Dollar as an Irrational Speculative Bubble: A Tale of Fundamentalists and Chartists , 1986 .

[35]  T. Lux.  Herd Behaviour, Bubbles and Crashes , 1995 .

[36]  Christophre Georges.  Learning Dynamics in an Artificial Currency Market , 2001 .

[37]  Gilles Teyssière,et al.  Microeconomic Models for Long Memory in the Volatility of Financial Time Series , 2001 .

[38]  Blake LeBaron,et al.  Stochastic Volatility as a Simple Generator of Financial Power-Laws and Long Memory , 2001 .

[39]  E. Pentecost,et al.  The Handbook of International Macroeconomics. , 1995 .