On the negative market volatility risk-premium: Bridging the gap between option returns and the pricing of options

Existing evidence indicates that (i) average returns of purchased delta-hedged options are negative, implying options are expensive, and (ii) volatility is the most important extra risk that is factored into option prices. Therefore, a natural extension is to explain the cross-section of average delta-hedged option returns in a stochastic volatility model. This paper solves this problem by introducing a measure of option overprice, which quantifies the impact on option prices of the volatility risk premium. It is an application of option-pricing in incomplete markets under stochastic volatility. An extensive numerical exercise shows the option overprice is consistent with the cross-section of average delta-hedged returns of calls, puts, and straddles reported by the literature for the S&P 500 index, except for expensive short-term out-of-the-money puts. In a stochastic volatility model, the volatility risk of at- and, especially, out-of-the-money calls and puts is several times larger than market volatility, which explains large negative volatility risk premiums if volatility risk is negative priced.