Option valuation via nonaffine dynamics with realized volatility

Abstract

This paper evaluates the improvement in option pricing brought about by realized volatility (RV) through nonaffine dynamics as advocated by Christoffersen et al. (2014). We complement their studies by developing a closed-form approximation of option pricing for the nonaffine models with RV, and then study the trade-off between the degradation in data fitting and the computational convenience offered by the analytical formula. Our studies confirm the literature that the nonaffine dynamics consistently outperform the affine in option pricing. In particular, we find that RV can significantly improve return fitting and option pricing through both affine and nonaffine models. For the affine models, we find strong evidence in favor of the RV information for both returns and options; for the nonaffine models, the evidence is less convincing for option pricing. We also provide additional new evidence that RV and nonaffine structures are equally competent at improving option pricing; moreover, these two features are complements rather than substitutes for GARCH option pricing, and the importance of one feature for option pricing is further enhanced when the other is present. All of these results are robust across moneyness, maturity, and volatility levels, and point to the necessity of including RV in nonaffine option pricing models.