We estimate a continuous-time model with stochastic volatility and dynamic crash probability for the S&P 500 index and find that market illiquidity dominates other factors in explaining the stock market crash risk. While the crash probability is time-varying, its dynamic depends only weakly on return variance once we include market illiquidity as an economic variable in the model.
Under very general conditions, the total quadratic variation of a jump-diffusion process can be decomposed into diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the underlying asset price exhibits volatility and jump intensity dynamics.
