A realized volatility approach to option pricing with continuous and jump variance components

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 which provides a rapidly moving volatility factor and improves on the fitting properties under the physical measure. The change of measure is performed by means of an exponentially affine pricing kernel which depends on an equity and two variance risk premia, associated with the continuous and jump components of realized volatility. Our choice preserves analytical tractability and offers a new way of estimating variance risk premia by combining high-frequency returns and option data in a multicomponent pricing model.