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Bifurcation routes to volatility clustering under evolutionary learning

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Author Info
Gaunersdorfer, Andrea
Hommes, Cars H.
Wagener, Florian O.O.

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Abstract

A simple asset pricing model with two types of boundedly rational traders, fundamentalists and chartists, is studied. Fractions of trader types change over time according to evolutionary learning, with chartists conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously and two generic mechanisms are proposed as an explanation: (1) coexistence of a stable steady state and a stable limit cycle, due to a so-called Chenciner bifurcation of the system and (2) intermittency and associated bifurcation routes to strange attractors. Economic intuition as to why these phenomena arise in nonlinear multi-agent evolutionary systems is provided.

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File URL: http://www.sciencedirect.com/science/article/B6V8F-4P777YW-2/1/e4ef0fa96d54119c06f4bb2eb16d5cbd
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Publisher Info
Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 67 (2008)
Issue (Month): 1 (July)
Pages: 27-47
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Handle: RePEc:eee:jeborg:v:67:y:2008:i:1:p:27-47

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References listed on IDEAS
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)
  2. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  3. William A. Brock, 1993. "Pathways to randomness in the economy: Emergent nonlinearity and chaos in economics and finance," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 8(1), pages 3-55.
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  4. 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.
  5. Blake LeBaron, 1999. "Evolution and Time Horizons in an Agent-Based Stock Market," Computing in Economics and Finance 1999 1342, Society for Computational Economics.
  6. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
  7. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers 01-014/1, Tinbergen Institute. [Downloadable!]
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  8. Xue-Zhong He & Carl Chiarella, 1999. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model," Computing in Economics and Finance 1999 223, Society for Computational Economics. [Downloadable!]
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  9. 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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  10. 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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  11. 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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  12. 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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  13. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," Journal of Business, University of Chicago Press, vol. 36, pages 394. [Downloadable!]
  14. 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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  15. 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)
  16. 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.
  17. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December. [Downloadable!] (restricted)
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  18. Tesfatsion, Leigh S. & Judd, Kenneth L., 2003. "Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics," Staff General Research Papers 10368, Iowa State University, Department of Economics. [Downloadable!]
  19. 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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  20. 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)
  21. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233 Elsevier. [Downloadable!] (restricted)
  22. 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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  23. George W. Evans & Seppo Honkapohja, 2008. "Learning and Macroeconomics," University of Oregon Economics Department Working Papers 2008-3, University of Oregon Economics Department. [Downloadable!]
  24. 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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  25. 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.
  26. J. Doyne Farmer & Shareen Joshi, 2000. "The Price Dynamics of Common Trading Strategies," Working Papers 00-12-069, Santa Fe Institute.
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  27. 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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  28. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute. [Downloadable!]
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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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Cited by:
(explanations, 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. 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. 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!]
  3. 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!]
  4. 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)
  5. 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:
  6. 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!]
  7. 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:
  8. Verbic, Miroslav, 2006. "Memory and Asset Pricing Models with Heterogeneous Beliefs," MPRA Paper 1261, University Library of Munich, Germany. [Downloadable!]
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