The cross section of options holds great promise for identifying return distributions and risk premia, but estimating dynamic option valuation models with latent state variables is challenging when using large option panels. We propose a particle Markov Chain Monte Carlo framework with a novel filtering approach and illustrate our method by estimating index option pricing models. Estimates of variance risk premiums, variance mean reversion, and higher moments differ from the literature. We show that these differences are due to the composition of the option sample. Restricting the option sample’s maturity dimension has the strongest impact on parameter inference and option fit in these models.

We propose no-arbitrage term structure models with volatility factors that follow GARCH processes. The models’ tractability is similar to canonical affine term structure models, but they fit yield volatility much better, especially for long-maturity yields. This improvement does not come at the expense of a deterioration in yield fit. Because of the improved volatility fit, the model performs substantially better in pricing Treasury futures options. We conclude that the specification of the volatility factors is critical. Modeling volatility as a function of (lagged) squared innovations to factors improves on models where volatility is a linear function of the factors.

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.