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The Dynamics of the Linear Random Farmer Model

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  • Rui Carvalho
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    Abstract

    On the framework of the Linear Farmer's Model, we approach the indeterminacy of agents' behaviour by associating with each agent an unconditional probability for her to be active at each time step. We show that Pareto tailed returns can appear even if value investors are the only strategies on the market and give a procedure for the determination of the tail exponent. Numerical results indicate that the returns' distribution is heavy tailed and volatility is clustered if trading occurs at the zero Lyapunov (critical) point.

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    File URL: http://arxiv.org/pdf/cond-mat/0107150
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0107150.

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    Date of creation: Jul 2001
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    Handle: RePEc:arx:papers:cond-mat/0107150

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    1. 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.
    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, vol. 49(2), pages 269-285, October.
    3. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March.
    4. 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.
    5. 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.
    6. J. Doyne Farmer, 1998. "Market Force, Ecology, and Evolution," Research in Economics 98-12-117e, Santa Fe Institute.
    7. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
    8. 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.
    9. Antonio Cabrales & Takeo Hoshi, 1993. "Heterogeneous beliefs, wealth accumulation and asset price dynamics," Economics Working Papers 55, Department of Economics and Business, Universitat Pompeu Fabra, revised Jun 1993.
    10. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
    11. J. Doyne Farmer & Shareen Joshi, 2000. "The Price Dynamics of Common Trading Strategies," Working Papers 00-12-069, Santa Fe Institute.
    12. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    13. repec:att:wimass:9624 is not listed on IDEAS
    14. Sarno, Lucio & Taylor, Mark P., 1999. "Moral hazard, asset price bubbles, capital flows, and the East Asian crisis:: the first tests," Journal of International Money and Finance, Elsevier, vol. 18(4), pages 637-657, August.
    15. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 3(2), pages 139-140, July.
    16. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    17. William A. Brock & Patrick de Fontnouvelle, 1996. "Expectational Diversity in Monetary Economies," Working Papers 96-11-084, Santa Fe Institute.
    18. 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.
    19. Day, R. & Huang, W., 1988. "Bulls, Bears And Market Sheep," Papers m8822, Southern California - Department of Economics.
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    Cited by:
    1. Franke, Reiner, 2009. "A prototype model of speculative dynamics with position-based trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1134-1158, May.
    2. Reiner Franke & Toichiro Asada, 2008. "Incorporating positions into asset pricing models with order-based strategies," Journal of Economic Interaction and Coordination, Springer, vol. 3(2), pages 201-227, December.

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