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Adaptive Beliefs and the volatility of asset prices

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Author Info
Andrea Gaunersdorfer (Vienna University)
Cars Hommes (CeNDEF, University of Amsterdam)
Florian Wagener (CeNDEF, University of 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. 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.

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Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Workshop Papers, January 2001 with number 5A.1.

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Date of creation: 04 Jan 2001
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Handle: RePEc:ams:cdws01:5a.1

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  1. Amilon, Henrik, 2005. "Estimation of an Adaptive Stock Market Model with Heterogeneous Agents," Working Paper Series 177, Sveriges Riksbank (Central Bank of Sweden). [Downloadable!]
  2. 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. [Downloadable!]
  3. 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!]
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  4. Henrik Amilon, 2003. "Estimation of an Adaptive Stock Market Model with Heterogeneous Agents," Research Paper Series 107, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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