A Jump and Smile Ride: Continuous and Jump Variance Risk Premia in Option Pricing

Stochastic and time-varying volatility models typically fail to correctly price out-of-the-money (OTM) put options at short maturity. We extend Realized Volatility option pricing models by adding a jump component estimated from high-frequency data and the associated risk premium. The inclusion of jumps provides a rapidly moving volatility factor, which improves on the fitting properties under the physical measure. The change of measure is performed adopting a Stochastic Discount Factor (SDF) with three risk premia: equity, and two variance risk premia related to the continuous and jump components. On the one hand, employing an SDF with multiple risk premia further improve the flexibility under risk neutral dynamics while preserving analytical tractability. On the other hand, it provides new way of separately estimate the continuous and jump variance risk premia by coherently combining high-frequency returns and option data in a multi-factor option pricing model. The empirical analysis illustrates the contribution of the jump factor to the pricing performance of Standard and Poor's 500 index OTM options. Finally, we apply our multi-factor model to estimate the time evolution of the two components of the variance risk premium and test their ability to predict future market returns.