Volatility and Expected Option Returns : A Note

Are options on more volatile assets expected to provide higher or lower return? Using analytics, we show the ambiguous nature of the answer when the volatility differential is due to the systematic/priced risk. Here the difference in the expected return of the assets also matters and has an effect on expected option return that is opposite to the case of idiosyncratic/unpriced risk. Our numerical results, based on more than 13 million parameter combinations, elaborate how the direction and magnitude of the net effect depends on the levels of asset beta and volatility and the moneyness and maturity of options. Accordingly, in analyzing the cross-section of returns on traded options, securities with embedded options, and other nonlinear derivatives, one should pay attention to the source of volatility differential, and the sample range/mix of betas, volatilities, and option moneyness and maturity