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Can a stochastic cusp catastrophe model explain stock market crashes?

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Listed author(s):
  • Barunik, J.
  • Vosvrda, M.

Abstract

This paper is the first attempt to fit a stochastic cusp catastrophe model to stock market data. We show that the cusp catastrophe model explains the crash of stock exchanges much better than other models. Using the data of U.S. stock markets we demonstrate that the crash of October 19, 1987, may be better explained by cusp catastrophe theory, which is not true for the crash of September 11, 2001. With the help of sentiment measures, such as the index put/call options ratio and trading volume (the former models the chartists, the latter the fundamentalists), we have found that the 1987 returns are bimodal, and the cusp catastrophe model fits these data better than alternative models. Therefore we may say that the crash has been led by internal forces. However, the causes for the crash of 2001 are external, which is also evident in much weaker presence of bifurcations in the data. In this case, alternative models explain the crash of stock exchanges better than the cusp catastrophe model.

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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 33 (2009)
Issue (Month): 10 (October)
Pages: 1824-1836

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Handle: RePEc:eee:dyncon:v:33:y:2009:i:10:p:1824-1836
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

Keywords: Stochastic cusp catastrophe Bifurcations Singularity Nonlinear dynamics Stock market crash;

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Cited by:

  1. Chiarella, Carl & He, Xue-Zhong & Zheng, Min, 2011. "An analysis of the effect of noise in a heterogeneous agent financial market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 148-162, January.
  2. Xu, Yan & Hu, Bin & Wu, Jiang & Zhang, Jianhua, 2014. "Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 100-108.
  3. Kukacka, Jiri & Barunik, Jozef, 2016. "Estimation of financial agent-based models with simulated maximum likelihood," FinMaP-Working Papers 63, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.

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