This paper examines the joint time series of the S&P500 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...

We model the S&P500 index options dynamics using the CGMY distribution, with independent "up" and "down" return jumps, and diffusive jump intensities. Allowing the up and down parts to be separately parameterised accounts for the dynamic smirk effect, without correlation between returns and...

We explore the optimal econometric specifications for fitting S&P500 options, in the very flexible CGMY class of models. We favour returns being ‘up’ and ‘down’ pure jumps with separate volatility ‘speeds’; and with down jumps having longer tails. This can account for the options...