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Modelování krachů na kapitálových trzích: aplikace teorie stochastických katastrof
[Stock market crashes modeling: stochastic cusp catastrophe application]

Author

Listed:
  • Miloslav Vošvrda
  • Jozef Baruník

Abstract

We show that the cusp catastrophe model explains the crash of stock exchanges much better than other models. On the data of U.S. stock markets we demonstrate that the crash of 1987 may be better explained by cusp catastrophe theory, which is not true for the crash of 2001. With the help of sentiment measures, such as index put/call options ratio and volume (the former models the proportion of the chartists, while the latter the fundamentalists), we have found that the 1987 returns are clearly bimodal and contain bifurcation flags. The cusp catastrophe model fits these data better then alternative models. Therefore we may say that the crash may have been led by internal forces. However, the causes for the crash of Sept. 11, 2001 are external, which is also evident in much weaker presence of bifurcations in the data. Thus alterantive models may be used for its explanation.

Suggested Citation

  • Miloslav Vošvrda & Jozef Baruník, 2008. "Modelování krachů na kapitálových trzích: aplikace teorie stochastických katastrof [Stock market crashes modeling: stochastic cusp catastrophe application]," Politická ekonomie, Prague University of Economics and Business, vol. 2008(6), pages 759-771.
    • Handle: RePEc:prg:jnlpol:v:2008:y:2008:i:6:id:662:p:759-771
    DOI: 10.18267/j.polek.662
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    References listed on IDEAS

    as
    1. Cobb, Loren, 1980. "Estimation Theory for the Cusp Catastrophe Model," MPRA Paper 37548, University Library of Munich, Germany, revised 05 Jun 2010.
    2. Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.
    3. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    nonlinear dynamics; cusp catastrophe; bifurcations; singularity; stock market crash;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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