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Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility


  • Jozef Barunik
  • Jiri Kukacka


This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in markets. We support our methodology by simulations where we also discuss the importance of stochastic noise and volatility in deterministic cusp catastrophe model. The methodology is empirically tested on almost 27 years of U.S. stock market evolution covering several important recessions and crisis periods. Due to the very long sample period we also develop a rolling estimation approach and we find that while in the first half of the period stock markets showed marks of bifurcations, in the second half catastrophe theory was not able to confirm this behavior. Results suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets.

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  • Jozef Barunik & Jiri Kukacka, 2013. "Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility," Papers 1302.7036,, revised May 2013.
  • Handle: RePEc:arx:papers:1302.7036

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    4. Wang, J., 2015. "Can a stochastic cusp catastrophe model explain housing market crashes?," CeNDEF Working Papers 15-12, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    5. Kukacka, Jiri & Kristoufek, Ladislav, 2020. "Do ‘complex’ financial models really lead to complex dynamics? Agent-based models and multifractality," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    6. Mohamed M. Mostafa, 2020. "Catastrophe Theory Predicts International Concern for Global Warming," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(3), pages 709-731, September.
    7. Dennis Wesselbaum, 2017. "Catastrophe theory and the financial crisis," Scottish Journal of Political Economy, Scottish Economic Society, vol. 64(4), pages 376-391, September.
    8. Bolgorian, Meysam, 2019. "Can a cusp catastrophe model describe the effect of sanctions on exchange rates?," Economics Discussion Papers 2019-2, Kiel Institute for the World Economy (IfW).

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