Dynamic Jump Intensities and Risk Premia: Evidence from S&P500 Returns and Options

Abstract

We build a new class of discrete time models where the distribution of daily returns is driven by two factors: dynamic volatility and dynamic jump intensity. Each factor has its own risk premium. The likelihood function for the models is available using analytical filtering, which makes them much easier to implement than most existing models. Estimating the models on S&P500 returns, we find that they significantly outperform standard models without jumps. We find very strong empirical support for time-varying jump intensities, and thus for flexible skewness and kurtosis dynamics. Compared to the risk premium on dynamic volatility, the risk premium on the dynamic jump intensity has a much larger impact on option prices. We confirm these findings using joint estimation on returns and large option samples, which is feasible in our class of models.

Keywords: compound Poisson process, option valuation, filtering, volatility jumps, jump risk premia, time-varying jump intensity, heteroskedasticity

JEL Classification: G12