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Time-Variation of Higher Moments in a Financial Market with Heterogeneous Agents: An Analytical Approach

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  • Simone Alfarano
  • Thomas Lux
  • Friedrich Wagner

Abstract

A growing body of recent literature allows for heterogenous trading strategies and limited rationality of agents in behavioral models of financial markets. More and more, this literature has been concerned with the explanation of some of the stylized facts of financial markets. It now seems that some previously mysterious time-series characteristics like fat tails of returns and temporal dependence of volatility can be observed in many of these models as macroscopic patterns resulting from the interaction among different groups of speculative traders. However, most of the available evidence stems from simulation studies of relatively complicated models which do not allow for analytical solutions. In this paper, this line of research is supplemented by analytical solutions of a simple variant of the seminal herding model introduced by Kirman [1993]. Embedding the herding framework into a simple equilibrium asset pricing model, we are able to derive closed-form solutions for the time-variation of higher moments as well as related quantities of interest enabling us to spell out under what circumstances the model gives rise to realistic behavior of the resulting time series --

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Bibliographic Info

Paper provided by Warwick Business School, Finance Group in its series Working Papers with number wpn06-01.

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Date of creation: 2006
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Handle: RePEc:wbs:wpaper:wpn06-01

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References

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  1. KIRMAN, Alan & TEYSSIÈRE, Gilles, . "Microeconomic models for long memory in the volatility of financial time series," CORE Discussion Papers RP -1593, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  3. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
  4. Ulrich Horst, 2005. "Financial price fluctuations in a stock market model with many interacting agents," Economic Theory, Springer, vol. 25(4), pages 917-932, 06.
  5. Levy, Moshe & Levy, Haim & Solomon, Sorin, 1994. "A microscopic model of the stock market : Cycles, booms, and crashes," Economics Letters, Elsevier, vol. 45(1), pages 103-111, May.
  6. Marco Raberto & Silvano Cincott & Sergio M. Focardi & Michele Marchesi, 2002. "Traders’ long-run wealth in an artificial financial market," Computing in Economics and Finance 2002 301, Society for Computational Economics.
  7. Follmer, Hans & Horst, Ulrich & Kirman, Alan, 2005. "Equilibria in financial markets with heterogeneous agents: a probabilistic perspective," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 123-155, February.
  8. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  9. Lux, Thomas & Schornstein, Sascha, 2002. "Genetic learning as an explanation of stylized facts of foreign exchange markets," Discussion Paper Series 1: Economic Studies 2002,29, Deutsche Bundesbank, Research Centre.
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  11. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
  12. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 510-41, June.
  13. W. Brian Arthur & John H. Holland & Blake LeBaron & Richard Palmer & Paul Taylor, 1996. "Asset Pricing Under Endogenous Expectation in an Artificial Stock Market," Working Papers 96-12-093, Santa Fe Institute.
  14. Alfarano, Simone & Lux, Thomas, 2005. "A noise trader model as a generator of apparent financial power laws and long memory," Economics Working Papers 2005,13, Christian-Albrechts-University of Kiel, Department of Economics.
  15. Stauffer, Dietrich & Sornette, Didier, 1999. "Self-organized percolation model for stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 271(3), pages 496-506.
  16. 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.
  17. 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, vol. 26(1), pages 19-49, August.
  18. Ramsey, James B., 1996. "On the existence of macro variables and of macro relationships," Journal of Economic Behavior & Organization, Elsevier, vol. 30(3), pages 275-299, September.
  19. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November.
  20. D. Challet & A. Chessa & M. Marsili & Y. -C. Zhang, 2000. "From Minority Games to real markets," Papers cond-mat/0011042, arXiv.org.
  21. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
  22. Carl Chiarella & Giulia Iori, 2002. "A simulation analysis of the microstructure of double auction markets," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 346-353.
  23. 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.
  24. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(02), pages 170-196, June.
  25. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
  26. E.R. Grannan & G.H. Swindle, 1994. "Contrarians and Volatility Clustering," Working Papers 94-03-010, Santa Fe Institute.
  27. 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.
  28. Egenter, E. & Lux, T. & Stauffer, D., 1999. "Finite-size effects in Monte Carlo simulations of two stock market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 250-256.
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