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Bifurcation Routes to Volatility Clustering

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  • Andrea Gaunersdorfer

    (University of Vienna)

  • Cars Hommes

    ()

  • Florian O.O. Wagener

    ()
    (University of Amsterdam)

Abstract

A simple asset pricing model with two types of adaptively learning traders,fundamentalists and technical analysts, is studied. Fractions of these tradertypes, which are both boundedly rational, change over time according toevolutionary learning, with technical analysts conditioning their forecastingrule upon deviations from a benchmark fundamental. Volatility clustering arisesendogenously in this model. Two mechanisms are proposed as an explanation. Thefirst is coexistence of a stable steady state and a stable limit cycle, whicharise as a consequence of a so-called Chenciner bifurcation of the system. Thesecond is intermittency and associated bifurcation routes to strange attractors.Both phenomena are persistent and occur generically in nonlinearmulti-agent evolutionary systems.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-015/1.

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Date of creation: 06 Feb 2001
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Handle: RePEc:dgr:uvatin:20010015

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  1. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1059-1096, September.
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  6. Gaunersdorfer, A. & Hommes, C.H., 2005. "A nonlinear structural model for volatility clustering," CeNDEF Working Papers, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance 05-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  7. 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, Elsevier, vol. 22(8-9), pages 1235-1274, August.
  8. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers, Tinbergen Institute 01-014/1, Tinbergen Institute.
  9. Granger, Clive W.J. & Teräsvirta, Timo, 1998. "A simple nonlinear time series model with misleading linear properties," Working Paper Series in Economics and Finance 237, Stockholm School of Economics.
  10. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers, Tinbergen Institute 01-014/1, Tinbergen Institute.
  11. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, Elsevier, vol. 96(1-2), pages 40-69, January.
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  16. 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, El Colegio de México, Centro de Estudios Económicos, vol. 8(1), pages 3-55.
  17. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, Elsevier, vol. 77(1), pages 1-14, November.
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  23. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2002. "Evolutionary dynamics in markets with many trader types," CeNDEF Working Papers, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance 02-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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