The Pricing of Jump Propagation: Evidence from Spot and Options Markets

This paper examines the joint time series of the S&P 500 index and its options with a two-factor Hawkes jump-diffusion model that captures jump propagation (i.e., the phenomenon in which the strike of one jump substantially raises the probability for more to follow). The propagation effect uncovered from the joint data is severe but short lived. On average, this component takes up more than two-thirds of the total jump risks. Our jump specification proves crucial not only in reconciling the dynamics implied from the joint data, but also in explaining the time series of option-implied volatility skew.