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Speculative behaviour and complex asset price dynamics: a global analysis

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  • Chiarella, Carl
  • Dieci, Roberto
  • Gardini, Laura

Abstract

This paper analyses the dynamics of a model of a share market consisting of two groups of traders: fundamentalists, who form rational expectations on the fundamental value of the asset, and chartists, who base their trading decisions on an analysis of past price trends. The model is reduced to a two-dimensional map whose dynamic behaviour is analysed in detail, particularly with respect to global dynamical behaviour. The dynamics are affected by parameters measuring the strength of fundamentalist demand and the speed with which chartists adjust their estimate of the trend to past price changes. The parameter space is characterized according to the local stability/instability of the equilibrium point as well as the noninvertibility of the map. The method of critical curves of noninvertible maps is used to understand and describe the range of global bifurcations that can occur. It is also shown how the knowledge of deterministic dynamics uncovered here can aid in understanding stochastic versions of the model.
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  • Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2002. "Speculative behaviour and complex asset price dynamics: a global analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 173-197, October.
    • Handle: RePEc:eee:jeborg:v:49:y:2002:i:2:p:173-197
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    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.
    2. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
    3. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    4. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
    5. Beja, Avraham & Goldman, M Barry, 1980. "On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-248, May.
    6. 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.
    7. Carl Chiarella & Roberto Dieci & Laura Gardini, 2003. "A Dynamic Analysis of Speculation Across Two Markets," Research Paper Series 89, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Goldman, M Barry & Beja, Avraham, 1979. "Market Prices vs. Equilibrium Prices: Returns' Variance, Serial Correlation, and the Role of the Specialist," Journal of Finance, American Finance Association, vol. 34(3), pages 595-607, June.
    9. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    10. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
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