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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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File URL: http://arxiv.org/pdf/1302.7036
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Paper provided by arXiv.org in its series Papers with number 1302.7036.

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Date of creation: Feb 2013
Date of revision: May 2013
Handle: RePEc:arx:papers:1302.7036
Contact details of provider: Web page: http://arxiv.org/

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  11. Cobb, Loren, 1980. "Estimation Theory for the Cusp Catastrophe Model," MPRA Paper 37548, University Library of Munich, Germany, revised 05 Jun 2010.
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