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Nonlocal onset of instability in an asset pricing model with heterogeneous agents

Author

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  • Gaunersdorfer, A.

    (University of Vienna)

  • Hommes, C.H.
  • Wagener, F.O.O.

    (Universiteit van Amsterdam)

Abstract

Empirical time series of financial market data, like day-to-day stock returns, exhibit the phenomenon that although usually tomorrow's price is unpredictable, the absolute value of the price change is correlated with the magnitude of past price changes; though the corresponding correlation coefficients are not very large, they are significantly different from zero. This phenomenon is known as `volatility clustering' in the financial liturature. In this note a micro-economic model of volatility clustering, introduced by Gaunersdorfer and Hommes, will be analysed. The deterministic skeleton of the model has a Chenciner bifurcation, and hence periodic points and invariant quasi-periodic circles coexisting with the `fundamental' equilibrium. Adding noise in form of stochastic supply shocks, volatility clustering is generated by the system jumping between the bases of attraction of the fundamental equilibrium (low volatility), and that of the non-fundamental attractor (high volatility).

Suggested Citation

  • Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2003. "Nonlocal onset of instability in an asset pricing model with heterogeneous agents," CeNDEF Working Papers 03-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    • Handle: RePEc:ams:ndfwpp:03-10
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    References listed on IDEAS

    as
    1. Gaunersdorfer, Andrea & Hommes, Cars H. & Wagener, Florian O.O., 2008. "Bifurcation routes to volatility clustering under evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 27-47, July.
    2. Andrea Gaunersdorfer & Cars Hommes, 2007. "A Nonlinear Structural Model for Volatility Clustering," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 265-288, Springer.
    3. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 95-132, February.
    4. Brock, William A. & de Fontnouvelle, Patrick, 2000. "Expectational diversity in monetary economies," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 725-759, June.
    5. Carl Chiarella & Xue-Zhong He, 2000. "Stability of Competitive Equilibria with Heterogeneous Beliefs and Learning," Research Paper Series 37, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Cees Diks & Roy van der Weide, 2003. "Continuous Beliefs Dynamics," Tinbergen Institute Discussion Papers 03-007/1, Tinbergen Institute.
    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, vol. 22(8-9), pages 1235-1274, August.
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    1. Gaunersdorfer, Andrea & Hommes, Cars H. & Wagener, Florian O.O., 2008. "Bifurcation routes to volatility clustering under evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 27-47, July.

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