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Bifurcation Routes to Volatility Clustering under Evolutionary Learning

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Author Info
Gaunersdorfer, A. (University of Vienna)
Hommes, C.H.
Wagener, F.O.O. () (Universiteit van Amsterdam)

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Abstract

A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically. Simple economic intuition why these phenomena arise in nonlinear multi-agent evolutionary systems is provided.

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Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 03-03.

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Date of creation: 2003
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Handle: RePEc:ams:ndfwpp:03-03

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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. 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. [Downloadable!] (restricted)
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  5. 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.
  6. Cars Hommes & Joep Sonnemans & Jan Tuinstra & Henk van de Velden, 2005. "Coordination of Expectations in Asset Pricing Experiments," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 18(3), pages 955-980. [Downloadable!] (restricted)
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  7. Blake LeBaron, 1999. "Evolution and Time Horizons in an Agent-Based Stock Market," Computing in Economics and Finance 1999 1342, Society for Computational Economics.
  8. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
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  10. 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)
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  13. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February. [Downloadable!] (restricted)
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  14. George W. Evans & Seppo Honkapohja, 2008. "Learning and Macroeconomics," University of Oregon Economics Department Working Papers 2008-3, University of Oregon Economics Department. [Downloadable!]
  15. Pintus, P. & Sands, D. & de Vilder, R., 1998. "On the Transition from Local Regular to Global Iregular Fluctuations," Papers 9818, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
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  16. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-38, August. [Downloadable!] (restricted)
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  17. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 40-69, January. [Downloadable!] (restricted)
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  18. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. " Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-64, December. [Downloadable!] (restricted)
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  19. 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.
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  20. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," Journal of Business, University of Chicago Press, vol. 36, pages 394. [Downloadable!]
  21. 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.
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  22. 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.
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  25. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November. [Downloadable!] (restricted)
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  26. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
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  28. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December. [Downloadable!] (restricted)
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  29. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
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  1. Orlando Gomes, . "Volatility, Heterogeneous Agents and Chaos," The Electronic Journal of Evolutionary Modeling and Economic Dynamics, IFReDE - Université Montesquieu Bordeaux IV. [Downloadable!]
    Other versions:
  2. Roberto Dieci & Ilaria Foroni & Laura Gardini & Xue-Zhong He, 2005. "Market Mood, Adaptive Beliefs and Asset Price Dynamics," Research Paper Series 162, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  3. Carl Chiarella & Xue-Zhong He & Duo Wang, 2004. "A Behavioural Asset Pricing Model with a Time-Varying Second Moment," Research Paper Series 141, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  4. Verbic, Miroslav, 2006. "Memory and Asset Pricing Models with Heterogeneous Beliefs," MPRA Paper 1261, University Library of Munich, Germany. [Downloadable!]
  5. Carl Chiarella & Roberto Dieci & Laura Gardini & Lucia Sbragia, 2008. "A Model of Financial Market Dynamics with Heterogeneous Beliefs and State-Dependent Confidence," Computational Economics, Springer, vol. 32(1), pages 55-72, September. [Downloadable!] (restricted)
  6. Carl Chiarella & Xue-Zhong He & Duo Wang, 2004. "Statistical Properties of a Heterogeneous Asset Price Model with Time-Varying Second Moment," Research Paper Series 142, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  7. Anufriev, M. & Panchenko, V., 2007. "Asset Prices, Traders' Behavior, and Market Design," CeNDEF Working Papers 07-14, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
    Other versions:
  8. 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. [Downloadable!]
    Other versions:
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