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 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 associated to the continuous and discontinuous components. Employing an SDF with multiple premia further improve the flexibility under risk neutral dynamics while preserving analytical tractability. It also provides new way of separately estimate variance risk premia by coherently combining high-frequency returns and option data in a multi-factor pricing model. The empirical analysis illustrates the influence of the jump factor on the pricing performances of Standard and Poor's 500 Index options.