Before revision:  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.
After revision:  Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use stochastic cusp catastrophe on the data normalized by the estimated volatility in the second step to study possible discontinuities in markets.