Time-Varying Jump Intensities and Fat Tail Dynamics : Evidence from S&P500 Returns and Options

We present a new discrete-time GARCH jump framework that allows for rich dynamics in higher moments by combining heteroskedastic processes with fat-tailed innovations in returns and volatility. We provide a tractable risk neutralization framework allowing for option valuation with separate modeling of risk premia for the jump and normal innovations. Our models can be estimated with ease on returns using standard maximum likelihood techniques, and joint estimation on returns and a large sample of options is also feasible. We find very strong empirical support for time-varying jump intensities, when estimating on S&P500 returns and on returns and options jointly