Moneyness, Underlying Asset Volatility, and the Cross-Section of Option Returns

We study the effect of an asset’s volatility on the expected returns of European options on the asset. Deriving predictions from a stochastic discount factor model, we show that the effect depends on whether variations in the asset’s volatility are driven by systematic or idiosyncratic volatility. While idiosyncratic-volatility-induced variations only affect the option elasticity, systematic volatility-induced variations also oppositely affect the expected return of the asset. Since the expected asset return (elasticity) effect dominates for options with more linear (non-linear) payoffs, systematic volatility prices sufficiently in-the-money (out-of-the-money) options with the opposite (same) sign as idiosyncratic volatility. Using single-stock calls as test assets, double-sorted portfolios and Fama-MacBeth (1973) regressions broadly support the model’s predictions.