Estimation of volatility of financial time series plays a crucial role in pricing derivatives. Volatility is often estimated from historical data; however, it is well known that volatility varies in time. We propose a method to choose a suitable length of historical data to estimate contemporary...

We show that the cusp catastrophe model explains the crash of stock exchanges much better than other models. On the data of U.S. stock markets we demonstrate that the crash of 1987 may be better explained by cusp catastrophe theory, which is not true for the crash of 2001. With the help of...