Abstract: Existing empirical investigations of jump dynamics in returns and volatility are fairly complicated due to the presence of latent factors. We present a new discrete-time frame-work that combines heteroskedastic processes with rich specifications of jumps in returns and volatility. We provide a tractable risk neutralization framework for this class of mod-els 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 index returns as well as on returns and options jointly. Our implementation allows for multiple jumps per day, and the data indicate support for this model feature, most notably on Black Monday in October 1987. Our results also confirm the importance of jump risk premia for option valuation: jumps cannot significantly improve the performance of option pricing models unless sizeable jump risk premia are present.