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The Stochastic Dynamics of Speculative Prices

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Author Info
Carl Chiarella () (School of Finance and Economics, University of Technology, Sydney)
Xue-Zhong He () (School of Finance and Economics, University of Technology, Sydney)
Min Zheng () (School of Finance and Economics, University of Technology, Sydney)

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Abstract

Within the framework of the heterogeneous agent paradigm, we establish a stochastic model of speculative price dynamics involving of two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the invariant measures of a random dynamical system. By conducting a stochastic bifurcation analysis, we examine the market impact of speculative behaviour. We show that, when the chartists use lagged price trends to form their expectations, the market equilibrium price can be characterised by a unique and stable invariant measure when the activity of the speculators is below a certain critical value. If this threshold is surpassed, the market equilibrium can be characterised by more than two invariant measures, of which one is completely stable, another is completely unstable and the remaining ones may exhibit various types of stability. Also, the corresponding stationary measure displays a significant qualitative change near the threshold value. We show that the stochastic model displays behaviour consistent with that of the underlying deterministic model. However, when the time lag in the formation of the price trends used by the chartists approaches zero, such consistency breaks down. In addition, the change in the stationary distribution is consistent with a number of market anomalies and stylised facts observed in financial markets, including a bimodal logarithmic price distribution and fat tails.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 208.

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Length: 47
Date of creation: 01 Dec 2007
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Handle: RePEc:uts:rpaper:208

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Related research
Keywords: heterogeneous agents; speculative behaviour; random dynamical systems; stochastic bifurcations; invariant measures; chartists;

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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. [Downloadable!] (restricted)
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    Other versions:
  4. He, Xue-Zhong & Li, Youwei, 2007. "Power-law behaviour, heterogeneity, and trend chasing," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3396-3426, October. [Downloadable!] (restricted)
  5. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
  6. Volker Bohm & Carl Chiarella, 2000. "Mean Variance Preferences, Expectations Formation, and the Dynamics of Random Asset Prices," Research Paper Series 46, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  7. Hommes, C.H., 2001. "Modeling the stylized facts in finance through simple nonlinear adaptive systems," CeNDEF Working Papers 01-06, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
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  10. Allen, Helen & Taylor, Mark P, 1990. "Charts, Noise and Fundamentals in the London Foreign Exchange Market," Economic Journal, Royal Economic Society, vol. 100(400), pages 49-59, Supplemen. [Downloadable!] (restricted)
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  16. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233 Elsevier. [Downloadable!] (restricted)
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  18. W.A. Brock, C.H. Hommes and F.O.O. Wagener, 2001. "Evolutionary dynamics in financial markets with many trader types," Computing in Economics and Finance 2001 119, Society for Computational Economics.
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  19. Robert J. Shiller, 1987. "Investor Behavior in the October 1987 Stock Market Crash: Survey Evidence," NBER Working Papers 2446, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  21. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier. [Downloadable!] (restricted)
    Other versions:
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