Institute of Information Theory and Automation

Publication details

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

Journal Article

Baruník Jozef, Kukačka Jiří

serial: Quantitative Finance vol.15, 6 (2015), p. 959-973

project(s): 612955, , GA402/09/0965, GA ČR, GA13-32263S, GA ČR

keywords: Stochastic cusp catastrophe model, Realized volatility, Bifurcations, Stock market crash

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abstract (eng):

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 theory 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 US 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 behaviour in the second half.


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Institute of Information Theory and Automation