Publication detail

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

Author(s): doc. PhDr. Jozef Baruník Ph.D.,
PhDr. Jiří Kukačka Ph.D.,
Type: IES Working Papers
Year: 2013
Number: 19
Published in: IES Working Papers 19/2013, published in QUANT FINANC
Publishing place: Prague
Keywords: stochastic cusp catastrophe model, realized volatility, bifurcations, stock market crash
JEL codes: C01, C53
Suggested Citation:
Grants: GAUK 588912 - Empirical Validation of Heterogeneous Agent Models SVV 267 504: Intensification of Doctoral Research in Economics and Finance: Extending Alternative Approaches to Economic Models
Abstract: 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.
Downloadable: WP_2013_19_Barunik_Kukacka
February 2023




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