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Can a stochastic cusp catastrophe model explain stock market crashes?

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  • 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.

Suggested Citation

  • Barunik, J. & Vosvrda, M., 2009. "Can a stochastic cusp catastrophe model explain stock market crashes?," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1824-1836, October.
    • Handle: RePEc:eee:dyncon:v:33:y:2009:i:10:p:1824-1836
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    1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    2. Evstigneev, Igor & Taksar, Michael, 2009. "Dynamic interaction models of economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 166-182, January.
    3. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    4. Mark A. Carlson, 2006. "A brief history of the 1987 stock market crash with a discussion of the Federal Reserve response," Finance and Economics Discussion Series 2007-13, Board of Governors of the Federal Reserve System (U.S.).
    5. Gennotte, Gerard & Leland, Hayne, 1990. "Market Liquidity, Hedging, and Crashes," American Economic Review, American Economic Association, vol. 80(5), pages 999-1021, December.
    6. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    7. Hołyst, Janusz A. & Kacperski, Krzysztof & Schweitzer, Frank, 2000. "Phase transitions in social impact models of opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 199-210.
    8. Boswijk, H. Peter & Hommes, Cars H. & Manzan, Sebastiano, 2007. "Behavioral heterogeneity in stock prices," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1938-1970, June.
    9. 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.
    10. Bauer, Christian & De Grauwe, Paul & Reitz, Stefan, 2009. "Exchange rate dynamics in a target zone--A heterogeneous expectations approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 329-344, February.
    11. Ho, Thomas S Y & Saunders, Anthony, 1980. "A Catastrophe Model of Bank Failure," Journal of Finance, American Finance Association, vol. 35(5), pages 1189-1207, December.
    12. Wang, Yaw-Huei & Keswani, Aneel & Taylor, Stephen J., 2006. "The relationships between sentiment, returns and volatility," International Journal of Forecasting, Elsevier, vol. 22(1), pages 109-123.
    13. Georges, Christophre, 2008. "Staggered updating in an artificial financial market," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2809-2825, September.
    14. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233, Elsevier.
    15. Finucane, Thomas J., 1991. "Put-Call Parity and Expected Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(4), pages 445-457, December.
    16. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    17. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
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    3. Kukacka, Jiri & Barunik, Jozef, 2017. "Estimation of financial agent-based models with simulated maximum likelihood," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 21-45.

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