Cusp Catastrophe Theory: Application to US Stock

We show that, the cusp catastrophe model explains the crash of stock exchanges much better than alternative linear and logistic models. On the data of U.S. stock markets we demonstrate that the crash of October 19, 1987 may be better explained by cusp catastrophe theory, which is not true for the crash of Sept. 11, 2001. With the help of sentiment measures, such as index put/call options ratio and trading volume (the former models the chartists, while the latter the fundamentalists), we have found that the 1987 returns are clearly bimodal and contain bifurcation flags. The cusp catastrophe model fits these data better than alternative models. Therefore we may say that the crash may have been led by internal forces. However, the causes for the crash of 2001 are external, which is also evident in much weaker presence of bifurcations in the data. Thus alternative models may be used for its explanation.