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The stochastic bifurcation behaviour of speculative financial markets

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

Abstract

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

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    1. 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.
    2. 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, January.
    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. 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.
    2. Dieci, Roberto & Schmitt, Noemi & Westerhoff, Frank, 2018. "Interactions between stock, bond and housing markets," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 43-70.
    3. Geoffrey Poitras & John Heaney, 2015. "Classical Ergodicity and Modern Portfolio Theory," Post-Print hal-03680380, HAL.
    4. 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.
    5. 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.
    6. Majewski, Adam A. & Ciliberti, Stefano & Bouchaud, Jean-Philippe, 2020. "Co-existence of trend and value in financial markets: Estimating an extended Chiarella model," Journal of Economic Dynamics and Control, Elsevier, vol. 112(C).
    7. 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.
    8. 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.
    9. Zou, Xiaoling & Ma, Pengyu & Zhang, Liren & Lv, Jingliang, 2022. "Dynamic properties for a stochastic food chain model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. 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, July-Dece.
    11. 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 1-2014.
    12. Adam Majewski & Stefano Ciliberti & Jean-Philippe Bouchaud, 2018. "Co-existence of Trend and Value in Financial Markets: Estimating an Extended Chiarella Model," Papers 1807.11751, arXiv.org.
    13. Poitras, Geoffrey, 2018. "The pre-history of econophysics and the history of economics: Boltzmann versus the marginalists," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 89-98.

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