Options Expected Returns: Variation by Moneyness and Maturity

This paper expands the literature on options expected returns by examining variation in call and put expected returns for different maturities and strike prices. A further specific goal is to comment on two empirical anomalies—the large negative returns to out-the-money (OTM) calls and puts—by examining which assumptions need to be relaxed for theoretical returns to match these empirical results. When all assumptions of Black-Scholes are enforced call option expected returns are positive, increasing in the strike price and decreasing in the time to maturity. Put returns are negative and increasing in the strike and maturity. Allowing skewness in the underlying returns generates results matching the empirical patterns described above. No assumptions about investor preferences are relaxed, suggesting that risk-seeking behavior is not a necessary condition for generating the empirical results. The result does, however, require either time-varying volatility in the underlier, or constant high volatility.