Are classical option pricing models consistent with observed option second-order moments? Evidence from high-frequency data

We suggest a joint analysis of ex-post intra-day variability in an option and its associated underlying asset market as a novel means of validating an option pricing model. For this purpose, we introduce the notion of option realized variance, by which we mean the cumulative variance realized by the sample path of successive option price observations. In concurrently observing the realized path of the underlying asset, we contrast option realized variance with the realized variance that would be implied from the underlying asset price path under certain model assumptions. In the empirical analysis, we focus on the implied volatility compensated Black-Scholes model and the Heston model. We find that neither model reconciles second-order moments in the option and the underlying asset market. The differences point to the existence of additional relevant pricing factors that affect option second-order moments. We thus corroborate findings made in option data of lower frequency.