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The stochastic bifurcation behaviour of speculative financial markets


  • Chiarella, Carl
  • He, Xue-Zhong
  • Wang, Duo
  • Zheng, Min


This paper establishes a continuous-time stochastic asset pricing model in a speculative financial market with fundamentalists and chartists by introducing a noisy fundamental price. By application of stochastic bifurcation theory, the limiting market equilibrium distribution is examined numerically. It is shown that speculative behaviour of chartists can cause the market price to display different forms of equilibrium distributions. In particular, when chartists are less active, there is a unique equilibrium distribution which is stable. However, when the chartists become more active, a new equilibrium distribution will be generated and become stable. The corresponding stationary density will change from a single peak to a crater-like density. The change of stationary distribution is characterized by a bimodal logarithm price distribution and fat tails. The paper demonstrates that stochastic bifurcation theory is a useful tool in providing insight into various types of financial market behaviour in a stochastic environment.

Suggested Citation

  • Chiarella, Carl & He, Xue-Zhong & Wang, Duo & Zheng, Min, 2008. "The stochastic bifurcation behaviour of speculative financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3837-3846.
  • Handle: RePEc:eee:phsmap:v:387:y:2008:i:15:p:3837-3846
    DOI: 10.1016/j.physa.2008.01.078

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    References listed on IDEAS

    1. Volker Böhm & Carl Chiarella, 2005. "Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 61-97.
    2. 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.
    3. Rheinlaender Thorsten & Steinkamp Marcus, 2004. "A Stochastic Version of Zeeman's Market Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(4), pages 1-25, December.
    4. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    5. Follmer, Hans & Horst, Ulrich & Kirman, Alan, 2005. "Equilibria in financial markets with heterogeneous agents: a probabilistic perspective," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 123-155, February.
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    Cited by:

    1. Xu, Yong & Feng, Jing & Li, JuanJuan & Zhang, Huiqing, 2013. "Stochastic bifurcation for a tumor–immune system with symmetric Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4739-4748.
    2. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Gregory Gagnon, 2012. "Exchange rate bifurcation in a stochastic evolutionary finance model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(1), pages 29-58, May.
    4. Dieci, Roberto & Schmitt, Noemi & Westerhoff, Frank H., 2018. "Interactions between stock, bond and housing markets," BERG Working Paper Series 133, Bamberg University, Bamberg Economic Research Group.
    5. Schmitt, Noemi & Westerhoff, Frank, 2017. "On the bimodality of the distribution of the S&P 500's distortion: Empirical evidence and theoretical explanations," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 34-53.
    6. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13.
    7. Wang, Luxuan & Niu, Ben & Wei, Junjie, 2016. "Dynamical analysis for a model of asset prices with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 297-313.


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