This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market … returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to … estimate daily realized volatility from returns. Then, we use stochastic cusp catastrophe on data normalized by the estimated …

The primary purpose of the study is to identify and measure the properties of asset bubbles, volatility clustering, and … empirical methods; the LPPL model to identify asset bubbles, the DCC-GARCH model to measure volatility clustering, and the … Diebold-Yilmaz volatility spillover index to measure the level of financial contagion. We provide robust evidence that during …