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A minimal noise trader model with realistic time series properties

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  • Alfarano, Simone
  • Lux, Thomas

Abstract

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. --

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Bibliographic Info

Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2003,15.

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Date of creation: 2003
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Handle: RePEc:zbw:cauewp:1125

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Keywords: Herd Behavior ; Speculative Dynamics ; Fat Tails ; Volatility Clustering;

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References

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  1. Gaunersdorfer, A. & Hommes, C.H., 2000. "A Nonlinear Structural Model for Volatility Clustering," CeNDEF Working Papers 00-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  2. 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, Elsevier, vol. 49(2), pages 269-285, October.
  3. P. Bak & M. Paczuski & M. Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Working Papers, Santa Fe Institute 96-09-075, Santa Fe Institute.
  4. Lux, Thomas & Schornstein, Sascha, 2005. "Genetic learning as an explanation of stylized facts of foreign exchange markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 169-196, February.
  5. I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics, EconWPA 9605004, EconWPA, revised 26 Sep 1996.
  6. B. LeBaron, 2001. "Stochastic volatility as a simple generator of apparent financial power laws and long memory," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(6), pages 621-631.
  7. LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 24(5-7), pages 679-702, June.
  8. J. Doyne Farmer & Shareen Joshi, 2000. "The price dynamics of common trading strategies," Papers cond-mat/0012419, arXiv.org.
  9. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B, University of Bonn, Germany 438, University of Bonn, Germany, revised Jul 1998.
  10. KIRMAN, Alan & TEYSSIÈRE, Gilles, 2002. "Microeconomic models for long-memory in the volatility of financial time series," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2002056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. D. Challet & A. Chessa & M. Marsili & Y. -C. Zhang, 2000. "From Minority Games to real markets," Papers cond-mat/0011042, arXiv.org.
  12. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, Elsevier, vol. 105(1), pages 131-159, November.
  13. Christophre Georges, 2001. "Learning Dynamics in an Artificial Currency Market," Computing in Economics and Finance 2001, Society for Computational Economics 31, Society for Computational Economics.
  14. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, Elsevier, vol. 62(2), pages 161-165, February.
  15. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B, University of Bonn, Germany 437, University of Bonn, Germany, revised Jul 1998.
  16. 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.
  17. B. B. Mandelbrot, 2001. "Stochastic volatility, power laws and long memory," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(6), pages 558-559.
  18. Arifovic, Jasmina & Gencay, Ramazan, 2000. "Statistical properties of genetic learning in a model of exchange rate," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 24(5-7), pages 981-1005, June.
  19. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 108(1), pages 137-56, February.
  20. Youssefmir, Michael & Huberman, Bernardo A., 1997. "Clustered volatility in multiagent dynamics," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 32(1), pages 101-118, January.
  21. Andersson, Michael K. & Eklund, Bruno & Lyhagen, Johan, 1999. "A Simple Linear Time Series Model with Misleading Nonlinear Properties," Working Paper Series in Economics and Finance 300, Stockholm School of Economics.
  22. 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, Elsevier, vol. 49(2), pages 217-239, October.
  23. Chen, Shu-Heng & Lux, Thomas & Marchesi, Michele, 2001. "Testing for non-linear structure in an artificial financial market," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 46(3), pages 327-342, November.
  24. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, American Finance Association, vol. 35(2), pages 235-48, May.
  25. De Vries, C.G. & Leuven, K.U., 1994. "Stylized Facts of Nominal Exchange Rate Returns," Papers, Purdue University, Krannert School of Management - Center for International Business Education and Research (CIBER) 94-002, Purdue University, Krannert School of Management - Center for International Business Education and Research (CIBER).
  26. Jeffrey A. Frankel & Kenneth A. Froot, 1986. "The Dollar as an Irrational Speculative Bubble: A Tale of Fundamentalisists," NBER Working Papers 1854, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. David Morton de Lachapelle & Damien Challet, 2009. "Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior," Papers 0912.4723, arXiv.org, revised Jun 2010.
  2. Gilles Dufrenot & Dominique Guegan & Anne Peguin-Feissolle, 2008. "Changing-regime volatility: a fractionally integrated SETAR model," Applied Financial Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(7), pages 519-526.
  3. Lux, Thomas, 2006. "Financial power laws: Empirical evidence, models, and mechanism," Economics Working Papers 2006,12, Christian-Albrechts-University of Kiel, Department of Economics.
  4. Heni Boubaker & Nadia Sghaier, 2014. "Wavelet based Estimation of Time- Varying Long Memory Model with Nonlinear Fractional Integration Parameter," Working Papers, Department of Research, Ipag Business School 2014-284, Department of Research, Ipag Business School.
  5. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 26(1), pages 19-49, August.
  6. repec:hal:journl:halshs-00185369 is not listed on IDEAS

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