The cusp catastrophe theory has been primarily developed as a deterministic theory for systems that may respond to continuous changes in a control variables by a discontinuous change. While most of the systems in behavioral sciences are subject to noise, and in behavioral finance moreover to time-varying volatility, it may be difficult to apply the theory in these fields. This paper addresses the issue and proposes a two-step estimation methodology, which will allow us to apply the catastrophe theory to  model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use the stochastic cusp catastrophe on the 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 the deterministic cusp model. The methodology is empirically tested on almost 27 years of U.S. stock market evolution covering several important recessions and crisis periods. Results suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets. We show that stock markets subject to noise and time-varying volatility shows strong bifurcation marks. Due to the very long sample period we also develop a rolling estimation approach , where we study the dynamics of the parameters and we find that while in the first half of the period stock markets showed strong marks of bifurcations, in the second half catastrophe theory was not able to confirm this behavior. Results may have an important implications for understanding the recent deep financial crisis of 2008.
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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The cusp catastrophe theory has been primarily developed as a deterministic theory for systems that may respond to continuous changes in a control variables by a discontinuous change. While most of the systems in behavioral sciences are subject to noise, and in behavioral finance moreover to time-varying volatility, it may be difficult to apply the theory in these fields. This paper addresses the issue and proposes
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stock market returns with time-varying volatility and
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the deterministic cusp
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Results suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets. We show that stock markets subject to noise and time-varying volatility shows strong bifurcation marks.
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, where we study the dynamics of the parameters
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may have an important implications for understanding the recent deep financial crisis of 2008.
suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets.