Understanding Risk Premia in Index Option Prices∗

We explore the reasons why out-of-the-money index puts trade on much higher implied volatilities than out-of-the-money calls. We develop a trading strategy that exploits the skew in implied volatility, and show that it has a simple interpretation. The pay-off to the strategy is identical to that on a swap whose floating leg is equal to the covariation between returns and changes in implied variance. The interpretation does not depend on any specific pricing model. We use the strategy to show that approximately half of the skew in implied volatility is due to the negative correlation between returns and implied volatility, and the other half can be considered a skew risk premium. We also find empirical evidence that this skew risk premium is closely related to the variance risk premium.