Variance swap premium under stochastic volatility and self-exciting jumps

We introduce a stochastic volatility model with self-exciting jump intensity to capture the change in pricing dynamic triggered by big negative stock returns. The stochastic variance and jump intensity, and their risk premium are estimated jointly from daily stock returns and option data over 2007-2010. The model is calibrated to cumulants implied from option prices instead of option prices directly. We find evidence that the time varying jump intensity plays a very important role in the sub-prime crisis and explained most of the risk premium, while in other calmer periods, stochastic variance accounts for most of the risk premium.