The cross-section of average delta-hedge option returns under stochastic volatility

Existing evidence indicates that average returns of purchased market-hedge S&P 500 index calls, puts, and straddles are non-zero but large and negative, which implies that options are expensive. This result is intuitively explained by means of volatility risk and a negative volatility risk premium, but there is a recent surge of empirical and analytical studies which also attempt to find the sources of this premium. An important question in the line of a priced volatility explanation is if a standard stochastic volatility model can also explain the cross-sectional findings of these empirical studies. The answer is fairly positive. The volatility elasticity of calls and puts is several times the level of market volatility, depending on moneyness and maturity, and implies a rich cross-section of negative average option returns—even if volatility risk is not priced heavily, albeit negative. We introduce and calibrate a new measure of option overprice to explain these results. This measure is robust to jump risk if jumps are not priced.