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A noise trader model as a generator of apparent financial power laws and long memory

  • Alfarano, Simone
  • Lux, Thomas

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 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 Kirman [1993]. The statistical analysis of simulated data points toward long-term dependence in the auto-correlations 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 like 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 as with the phenomenological volatility models analyzed in LeBaron [2001], the usual statistical tests are not able to distinguish between true or pseudo-scaling laws in the dynamics of our artificial market

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Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2005,13.

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Date of creation: 2005
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Handle: RePEc:zbw:cauewp:3559
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  1. J. Doyne Farmer & Shareen Joshi, 2000. "The price dynamics of common trading strategies," Papers cond-mat/0012419, arXiv.org.
  2. B. LeBaron, 2001. "Stochastic volatility as a simple generator of apparent financial power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 621-631.
  3. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-48, May.
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  5. Chen, Shu-Heng & Yeh, Chia-Hsuan, 2002. "On the emergent properties of artificial stock markets: the efficient market hypothesis and the rational expectations hypothesis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 217-239, October.
  6. Friedrich Wagner & Thomas Lux & Simone Alfarano, 2005. "Time-Variation of Higher Moments in a Financial Market with Heterogeneous Agents: An Analytical Approach," Working Papers wp05-02, Warwick Business School, Finance Group.
  7. Wagner, Friedrich, 2003. "Volatility cluster and herding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 607-619.
  8. P. Bak & M. Paczuski & Martin Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Cowles Foundation Discussion Papers 1132, Cowles Foundation for Research in Economics, Yale University.
  9. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
  10. Alan P. Kirman, Gilles Teyssiere, 2001. "Microeconomic Models for Long-Memory in the Volatility of Financial Time Series," Computing in Economics and Finance 2001 221, Society for Computational Economics.
  11. Lux, Thomas & Schornstein, Sascha, 2003. "Genetic learning as an explanation of stylized facts of foreign exchange markets," Economics Working Papers |aEconomics working paper, Christian-Albrechts-University of Kiel, Department of Economics.
  12. Simone Alfarano & Thomas Lux, 2002. "A minimal noise trader model with realistic time series," Computing in Economics and Finance 2002 317, Society for Computational Economics.
  13. Iori, Giulia, 2002. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 269-285, October.
  14. LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June.
  15. D. Challet & A. Chessa & M. Marsili & Y-C. Zhang, 2001. "From Minority Games to real markets," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 168-176.
  16. I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics 9605004, EconWPA, revised 26 Sep 1996.
  17. Granger, Clive W.J. & Teräsvirta, Timo, 1998. "A simple nonlinear time series model with misleading linear properties," SSE/EFI Working Paper Series in Economics and Finance 237, Stockholm School of Economics.
  18. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
  19. B. B. Mandelbrot, 2001. "Stochastic volatility, power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 558-559.
  20. Andersson, Michael K. & Eklund, Bruno & Lyhagen, Johan, 1999. "A Simple Linear Time Series Model with Misleading Nonlinear Properties," SSE/EFI Working Paper Series in Economics and Finance 300, Stockholm School of Economics.
  21. De Vries, C.G. & Leuven, K.U., 1994. "Stylized Facts of Nominal Exchange Rate Returns," Papers 94-002, Purdue University, Krannert School of Management - Center for International Business Education and Research (CIBER).
  22. Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2000. "Bifurcation Routes to Volatility Clustering," CeNDEF Working Papers 00-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  23. Youssefmir, Michael & Huberman, Bernardo A., 1997. "Clustered volatility in multiagent dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 32(1), pages 101-118, January.
  24. Gaunersdorfer, A. & Hommes, C.H., 2005. "A nonlinear structural model for volatility clustering," CeNDEF Working Papers 05-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  25. Georges, Christophre, 2006. "Learning with misspecification in an artificial currency market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(1), pages 70-84, May.
  26. Arifovic, Jasmina & Gencay, Ramazan, 2000. "Statistical properties of genetic learning in a model of exchange rate," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 981-1005, June.
  27. Shu-Heng Chen & Thomas Lux & Michele Marchesi, 1999. "Testing for Non-Linear Structure in an Artificial Financial Market," Discussion Paper Serie B 447, University of Bonn, Germany.
  28. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
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