This paper applies the Bates (RFS, 2006) methodology to the problem of estimating and filtering time- changed Lévy processes, using daily data on U.S. stock market excess returns over 1926-2006. In contrast to density-based filtration approaches, the methodology recursively updates the...

This paper examines the equilibrium when negative stock market jumps (crashes) can occur, and investors have heterogeneous attitudes towards crash risk. The less crash-averse insure the more crash-averse through the options markets that dynamically complete the economy. The resulting equilibrium...

This paper explores whether affine models with volatility jumps estimated on intradaily S&P 500 futures data over 1983 to 2008 can capture major daily outliers such as the 1987 stock market crash. Intradaily jumps in futures prices are typically small; self-exciting but short-lived volatility...