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

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Author Info
Alfarano, Simone
Lux, Thomas
Wagner, Friedrich

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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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Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics working papers with number 2005,14.

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Date of creation: 2005
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Handle: RePEc:zbw:cauewp:3560

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Lux, T. and 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.
  2. Alan Kirman & Gilles Teyssière, 2002. "Microeconomic Models for Long Memory in the Volatility of Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 5(4), pages 1083-1083. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  6. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. 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.
  11. 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. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
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  1. 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. [Downloadable!]
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