ABSTRACT We propose a novel factor model for option returns. Option exposures are estimated nonparametrically, and factor risk premia can vary nonlinearly with states. The model is estimated using regressions with minimal assumptions on factor and option return dynamics. We estimate the model using index options to characterize the conditional risk premia for factors of interest, such as the market return, market variance, tail and intermediary risk factors, higher moments, and the VIX term structure slope. Together, market return and variance explain more than 90% of option return variation. Unconditionally, the magnitude of the variance risk premium is plausible. It displays pronounced time variation, spikes during crises, and always has the expected sign.

We develop a structural credit risk model, which allows us to price equity/credit indices and their options through the asset dynamics of index constituents. We estimate the model via MLE and find that equity and credit index option prices are well explained out-of-sample. Contrary to recent empirical findings, the two option markets are not inconsistently priced through the lens of our model. Returns on both options, while extreme, do not indicate any evidence of mispricing. Our analysis suggests that jointly addressing the pricing of various instruments requires properly attributing three different sources of systematic risk: asset, variance, and jump risks.