A Bayesian analysis of time-varying jump risk in S&P 500 returns and options

We examine time-varying jump risk for modeling stock price dynamics and cross-sectional option prices. We explore jump-diffusion specifications with two independently evolving pro-cesses for stochastic volatility and jump intensity, respectively. We explicitly impose time-series consistency in model estimation using a Markov Chain Monte Carlo (MCMC) method. We find that both the jump size and standard deviation of jump size premia are more prominent under time-varying jump risk. Simultaneous jumps in returns and volatility help reconcile the time series of returns, volatility, and jump intensities. Finally, independent time-varying jump intensities improve the cross-sectional fit of option prices, especially at longer maturities.