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

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  • Baruník, Jozef
  • Kukacka, Jiri

Abstract

This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to estimate daily realized volatility from returns. Then, we use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in the markets. We support our methodology through simulations in which we discuss the importance of stochastic noise and volatility in a deterministic cusp catastrophe model. The methodology is empirically tested on nearly 27 years of U.S. stock market returns covering several important recessions and crisis periods. While we find that the stock markets showed signs of bifurcation in the first half of the period, catastrophe theory was not able to confirm this behavior in the second half. Translating the results, we find that the U.S. stock market's downturns were more likely to be driven by the endogenous market forces during the first half of the studied period, while during the second half of the period, the exogenous forces seem to be driving the market's instability. The results suggest that the proposed methodology provides an important shift in the application of catastrophe theory to stock markets.

Suggested Citation

  • Baruník, Jozef & Kukacka, Jiri, 2014. "Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility," FinMaP-Working Papers 15, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
  • Handle: RePEc:zbw:fmpwps:15
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    References listed on IDEAS

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    Cited by:

    1. Dennis Wesselbaum, 2017. "Catastrophe theory and the financial crisis," Scottish Journal of Political Economy, Scottish Economic Society, vol. 64(4), pages 376-391, September.
    2. Michael S. Harr'e & Adam Harris & Scott McCallum, 2019. "Singularities and Catastrophes in Economics: Historical Perspectives and Future Directions," Papers 1907.05582, arXiv.org.
    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.
    4. Michael S. Harr'e, 2018. "Multi-agent Economics and the Emergence of Critical Markets," Papers 1809.01332, arXiv.org.
    5. 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.
    6. 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).
    7. 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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    Keywords

    stochastic cusp catastrophe model; realized volatility; bifurcations; stock market crash;

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