Volatility and Expected Option Returns

Abstract

We analyze the relation between expected option returns and the volatility of the underlying securities. In the Black-Scholes-Merton and stochastic volatility models, the expected return from holding a call (put) option is a decreasing (increasing) function of the volatility of the underlying. These predictions are strongly supported by the data. In the cross-section of stock option returns, returns on call (put) option portfolios decrease (increase) with underlying stock volatility. This strong negative (positive) relation between call (put) option returns and volatility is not due to cross-sectional variation in expected stock returns. It holds in various option samples with different maturities and moneyness, and it is robust to alternative measures of underlying volatility and different weighting methods. Time-series evidence also supports the predictions from option pricing theory: Future returns on S&P 500 index call (put) options are negatively (positively) related to S&P 500 index volatility.