Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T12:49:01.894Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOISE TRADER MODEL AS A GENERATOR OF APPARENT FINANCIAL POWER LAWS AND LONG MEMORY

Published online by Cambridge University Press:  05 July 2007

SIMONE ALFARANO  and
THOMAS LUX
SIMONE ALFARANO
Affiliation:
University of Kiel
THOMAS LUX
Affiliation:
University of Kiel
Get access Rights & Permissions [Opens in a new window]

Abstract

In various agent-based models, the stylized facts of financial markets (unit roots, fat tails, and volatility clustering) have been shown to emerge from the interactions of agents. However, the complexity of these models often limits their analytical accessibility. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing these ubiquitous statistical properties. The simplicity of our approach permits us to derive some analytical insights using concepts from statistical mechanics. In our model, traders are divided into two groups, fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by A. Kirman (Ants, rationality, and recruitment, Quarterly Journal of Economics 108, 137–156, 1993). The statistical analysis of simulated data points toward long-term dependence in the autocorrelations of squared and absolute returns and hyperbolic decay in the tail of the distribution of raw returns, both with estimated decay parameters in the same range as those of empirical data. Theoretical analysis, however, excludes the possibility of “true” scaling behavior because of the Markovian nature of the underlying process and the boundedness of returns. The model, therefore, only mimics power law behavior. Similarly to the phenomenological volatility models analyzed by LeBaron (Stochastic volatility as a simple generator of apparent financial power laws and long memory, Quantitative Finance 1, 621–631, 2001), the usual statistical tests are not able to distinguish between true and pseudo-scaling laws in the dynamics of our artificial market.

Keywords

Herd BehaviorSpeculative DynamicsFat TailsVolatility Clustering
Type
ARTICLES
Information
Macroeconomic Dynamics , Volume 11 , Supplement S1: Interacting Agents and Market Behavior , November 2007 , pp. 80 - 101
Copyright
© 2007 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alfarano S., T. Lux, & F. Wagner 2005a Estimation of agent-based models: The case of an asymmetric herding model. Computational Economics 26, 19– 49.Google Scholar
Alfarano S., T. Lux, & F. Wagner 2005b Time-Variation of Higher Moments in a Financial Market with Heterogeneous Agents: An analytical approach. Working paper, University of Kiel.
Anderson M. K., B. Eklund, & J. Lyhagen 1999 A simple linear time series model with misleading nonlinear properties. Economics Letters 65, 281– 284.Google Scholar
Arifovic J. & R. Gencay 2000 Statistical properties of genetic learning in a model of exchange rate. Journal of Economic Dynamics and Control 24, 981– 1006.Google Scholar
Bak P., M. Paczuski, & M. Shubik 1997 Price variations in a stock market with many agents. Physica A 246, 430– 453.Google Scholar
Beja A. & M. B. Goldman 1980 On the dynamic behavior of prices in disequilibrium. Journal of Finance 35, 235– 248.Google Scholar
Bornholdt S. 2001 Expectation bubbles in a spin model of markets: Intermittency from frustation across scales. International Journal of Modern Physics C 12, 667– 674.Google Scholar
Challet D., A. Chessa, M. Marsili, & Y.-C. Zhang 2001 From minority game to the real markets. Quantitative Finance 1, 168– 176.Google Scholar
Chen S. H., T. Lux, & M. Marchesi 2001 Testing for nonlinear structure in an “artificial” financial market. Journal of Economic Behavior and Organization 46, 327– 342.Google Scholar
Chen S. H. & C. H. Yeh 2002 On the emergent properties of artificial stock markets: The efficient market hypothesis and the rational expectations hypothesis. Journal of Economic Behavior and Organization 49, 217– 239.Google Scholar
Day R. H. & W. Huang 1990 Bulls, bears, and market sheep. Journal of Economic Behavior and Organization 14, 299– 329.Google Scholar
de Vries C. G. 1994 Stylized facts of nominal exchange rate returns. In F. van der Ploeg (ed.), The Handbook of International Macroeconomics, pp 348– 389. Oxford: Blackwell.
Diebold F. X. & A. Inoue 2001 Long memory and regime switching. Journal of Econometrics 105, 131– 159.Google Scholar
Eguiluz V. M. & M. G. Zimmermann 2000 Transmission of information and herd behaviour: An application to financial markets. Physical Review Letters 85, 5659– 5662.Google Scholar
Farmer J. D. & S. Joshi 2002 The price dynamics of common trading strategies. Journal of Economic Behavior and Organization 49, 149– 171.Google Scholar
Feller W. 1971 An Introduction to Probability Theory and Its Applications. New York: Wiley.
Frankel J. & K. A. Froot 1986 The dollar as an irrational speculative bubble: A table of fundamentalists and chartists. Marcus Wallenberg Papers in International Finance 1, 27– 55.Google Scholar
Gardiner C. W. 2003 Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, third edition. Berlin: Springer.
Gaunersdorfer A. & C. Hommes 2005 A nonlinear structural model for volatility clustering. In G. Teyssifiere & A. Kirman (eds.), Long Memory in Economics. Berlin: Springer.
Gaunersdorfer A., C. H. Hommes, & F. O. O. Wagener 2000 Bifurcation Routes to Volatility Clustering. http://finance2.bwl.univie.ac.at/research/papers/ghw.zip. Accessed June, 2003.Google Scholar
Georges C. 2005 Learning with misspecification in an artificial currency market. Journal of Economic Behavior and Organization, in press.Google Scholar
Geweke J. & S. Porter-Hudak 1983 The estimation and application of long memory time series models. Journal of Time Series Analysis 4, 221– 238.Google Scholar
Granger C. W. J. & T. Teräsvirta 1999 A simple nonlinear time series model with misleading linear properties. Economic Letters 62, 161– 165.Google Scholar
Hill B. M. 1975 A simple general approach to inference about the tail of a distribution. Annals of Statistics 3, 1163– 1173.Google Scholar
Iori G. 2002 A micro-simulation traders' activity in the stock market: The rule of heterogeneity, agents' interactions and trade friction. Journal of Economic Behaviour and Organisation 49, 269– 285.Google Scholar
Kelly F. 1979 Reversibility and Stochastic Networks. New York: Wiley.
Kirman A. 1993 Ants, rationality, and recruitment. Quarterly Journal of Economics 108, 137– 156.Google Scholar
Kirman A. & G. Teyssifière 2002 Microeconomic models for long memory in the volatility of financial time series. Studies in Nonlinear Dynamics and Econometrics 5, 137– 156.Google Scholar
LeBaron B. 2000 Agent based computational finance: Suggested readings and early research. Journal of Economic Dynamics and Control 24, 679– 702.Google Scholar
LeBaron B. 2001 Stochastic volatility as a simple generator of apparent financial power laws and long memory. Quantitative Finance 1, 621– 631.Google Scholar
Lobato I. N. & N. E. Savin 1998 Real and spurious long-memory properties of stock market data. Journal of Business and Economics Statistics 16, 261– 283.Google Scholar
Lux T. 1995 Herd behaviour, bubbles and crashes. Economic Journal 105, 881– 896.Google Scholar
Lux T. 2005 Financial power laws: Empirical evidence, models, and mechanisms. In C. Cioffi-Revilla (ed.), Power Laws in Social Sciences: Discovering Complexity and Non-equilibrium in the Social Universe. In preparation.
Lux T. & M. Ausloos 2002 Market uctuations I: Scaling, multiscaling and their possible origins. In A. Bunde, J. Kropp, & H. J. Schellnhuber (eds.), Theories of Disaster—Scaling Laws Governing Weather, Body, and Stock Market Dynamics, pp. 373– 409. Berlin: Springer.
Lux T. & M. Marchesi 1999 Scaling and criticality in a stochastic multi-agent model of a financial market. Nature 397, 498– 500.Google Scholar
Lux T. & M. Marchesi 2000 olatility clustering in financial markets: A micro-simulation of interacting agents. International Journal of Theoretical and Applied Finance 3, 67– 702.Google Scholar
Lux T. & S. Schornstein 2005 Genetic learning as an explanation of stylized facts of foreign exchange markets. Journal of Mathematical Economics 41, 169– 196.Google Scholar
Palmer R. G., W. B. Arthur, J. H. Holland, B. LeBaron, & P. Tayler 1994 Artificial economic life: A simple model of stock market. Physica D 75, 264– 274.Google Scholar
Peng C. K., S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, & A. L. Goldberger 1994 Mosaic organization of DNA nucleotidies. Physical Review E 49, 1685– 1689.Google Scholar
Takayasu H., H. Miura, T. Hirabayashi, & K. Hamada 1992 Statistical properties of deterministic threshold elements—The case of market price. Physica A 184, 127– 134.Google Scholar
Wagner F. 2003 Volatility cluster and herding. Physica A 322, 607– 619.Google Scholar
Youssefmir M. & A. Huberman 1997 Clustered volatility in multiagent dynamics. Journal of Economic Behavior and Organization 32, 101– 118.Google Scholar