While other commonly used aggregate stock market volatility measures are strongly priced in the cross-section of stock returns, the empirical evidence is considerably weaker for option-implied market volatility. The differential pricing of market volatility risks is hard to reconcile with existing theories, but potentially consistent with partial segmentation between index options and equity markets. The comovement between option-implied volatility and other stock volatility measures contains valuable information about equity and index option market segmentation. The two markets exhibit time-varying segmentation, but have become more integrated in recent years, partly due to declining transaction costs and broader participation in options market.

Expected returns on market volatility, which can be obtained from VIX futures prices in closed form using standard models, positively predict subsequent realized volatility returns. Volatility returns are negative on average. Following increases in volatility, expected volatility returns and subsequent realized volatility returns become more negative. Because realized volatility returns are negatively correlated with index returns, expected volatility returns also negatively predict S&P 500 index returns, but these results are less significant. The results are robust to a wide range of variations in the empirical setup and to small-sample biases.

Existing studies relate the puzzling low average returns on out-of-the-money (OTM) index call and put options to nonstandard preferences. We argue the low option returns are primarily due to the pricing of market volatility risk. When volatility risk is priced, expected option returns match the realized average option returns. Moreover, consistent with its theoretical effect on expected option returns, the volatility risk premium is positively related to future index option returns and this relationship is stronger for OTM options and at-the-money straddles. Finally, we find the jump risk premium contributes to some portion of OTM put option returns.

We analyze the relation between expected option returns and the volatility of the underlying securities. The expected return from holding a call (put) option is a decreasing (increasing) function of the volatility of the underlying. These predictions are supported by the data. In the cross section of equity option returns, returns on call (put) option portfolios decrease (increase) with underlying stock volatility. This finding is not due to cross-sectional variation in expected stock returns. It holds in various option samples with different maturities and moneyness, and is robust to alternative measures of underlying volatility and different weighting methods.

The conditional covariance between the market return and its variance, which we refer to as the leverage effect, is positively related to the variance risk premium. It contains incremental information about the variance risk premium after controlling for other return moments and additional variables suggested by the literature as determinants of the variance risk premium. This empirical finding is supported by theory: the pricing of volatility risk is the economic channel behind the strong positive relation between the two variables. We use this relation to construct a time series of the variance risk premium dating back to 1926. (JEL G12, G13) Received February 7, 2020; editorial decision September 01, 2021.