The stochastic bifurcation behaviour of speculative financial markets
AbstractThis 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 387 (2008)
Issue (Month): 15 ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Heterogeneous agents; Speculative behaviour; Random dynamical systems; Stochastic bifurcations; Invariant measures;
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- Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
- 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.
- 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.
- Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-48, May.
- Gregory Gagnon, 2012. "Exchange rate bifurcation in a stochastic evolutionary finance model," Decisions in Economics and Finance, Springer, vol. 35(1), pages 29-58, May.
- 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.
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