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Time-variation of higher moments in a financial market with heterogeneous agents: An analytical approach

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  • Alfarano, Simone
  • Lux, Thomas
  • Wagner, Friedrich

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 assumed interaction 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 framework, 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 Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2006,16.

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Date of creation: 2006
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Handle: RePEc:zbw:cauewp:5163

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  1. 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, Elsevier, vol. 268(1), pages 250-256.
  2. 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.
  3. Alan P. Kirman, Gilles Teyssiere, 2001. "Microeconomic Models for Long-Memory in the Volatility of Financial Time Series," Computing in Economics and Finance 2001, Society for Computational Economics 221, Society for Computational Economics.
  4. 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.
  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, Elsevier, vol. 49(2), pages 217-239, October.
  6. 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, Elsevier, vol. 33(2), pages 143-165, January.
  7. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 14(3), pages 299-329, December.
  8. 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.
  9. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 4(02), pages 170-196, June.
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  14. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 105(431), pages 881-96, July.
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  17. Carl Chiarella & Giulia Iori, 2002. "A simulation analysis of the microstructure of double auction markets," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(5), pages 346-353.
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  19. Ramsey, James B., 1996. "On the existence of macro variables and of macro relationships," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 30(3), pages 275-299, September.
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  21. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 104(3), pages 510-41, June.
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  23. 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.
  24. E.R. Grannan & G.H. Swindle, 1994. "Contrarians and Volatility Clustering," Working Papers, Santa Fe Institute 94-03-010, Santa Fe Institute.
  25. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 22(1), pages 1-38, November.
  26. 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, Santa Fe Institute 96-12-093, Santa Fe Institute.
  27. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 23(9-10), pages 1487-1516, September.
  28. Levy, Moshe & Levy, Haim & Solomon, Sorin, 1994. "A microscopic model of the stock market : Cycles, booms, and crashes," Economics Letters, Elsevier, Elsevier, vol. 45(1), pages 103-111, May.
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