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Adaptive Beliefs and the volatility of asset prices

Author

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  • Andrea Gaunersdorfer

    (Vienna University)

  • Cars Hommes

    (CeNDEF, University of Amsterdam)

  • Florian Wagener

    (CeNDEF, 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 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. In a recent paper Gaunersdorfer and Hommes have shown that asset prices switch irregularly between two different regimes -- close to the fundamental price fluctuations with low volatility, and periods of persistent deviations from fundamentals where the market is dominated by technical trading -- thus, creating time varying volatility with autocorrelation structure similar to that observed in real financial data. Gaunersdorfer, Hommes, and Wagener propose two mechanisms 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 in nonlinear multi-agent evolutionary systems. Further, in the case of a constant fundamental value we obtain return series with statistical properties closest to those of real data when EMH-believers and trend followers interact. In that case price series are close to having a unit root. In an extension of the model we replace the iid dividend process by a non-stationary process.

Suggested Citation

  • Andrea Gaunersdorfer & Cars Hommes & Florian Wagener, 2001. "Adaptive Beliefs and the volatility of asset prices," CeNDEF Workshop Papers, January 2001 5A.1, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:cdws01:5a.1
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    References listed on IDEAS

    as
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    Cited by:

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    2. Anne Peguin-Feissolle & Gilles Dufrénot & Dominique Guegan, 2006. "Changing-regime volatility : A fractionally integrated SETAR model," Working Papers halshs-00410540, HAL.
    3. 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.
    4. Fabio Dercole & Davide Radi, 2014. "Does the "uptick rule" stabilize the stock market? Insights from Adaptive Rational Equilibrium Dynamics," Papers 1405.7747, arXiv.org.
    5. Constantinos VORLOW & Antonios ANTONIOU & Catherine KYRTSOU, 2004. "Surrogate Data Analysis and Stochastic Chaotic Modelling: Application to Stock Exchange Returns Series," Computing in Economics and Finance 2004 27, Society for Computational Economics.
    6. Boubaker Heni & Canarella Giorgio & Miller Stephen M. & Gupta Rangan, 2017. "Time-varying persistence of inflation: evidence from a wavelet-based approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(4), pages 1-18, September.
    7. Dercole, Fabio & Radi, Davide, 2020. "Does the “uptick rule” stabilize the stock market? Insights from adaptive rational equilibrium dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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