Before revision: 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.
After revision: This paper develops a two-step estimation methodology, which will allow us to apply the catastrophe theory to model stock market crashes.