Vol, Skew, and Smile Trading

We show how a three-strike option portfolio can be used to either trade the difference between the instantaneous variance rate and the implied variance rate, the difference between the instantaneous covariation rate and the implied slope, or the difference between this instantaneous variance rate of volatility and the implied convexity. We label each one of these strategies as vol, skew and smile trades. Our results yield precise financial interpretations of particular measures of the level, slope, and curvature of a BMS implied variance curve. We provide empirical evidence that the average returns of the vol and smile (skew) trades are negative (positive) and that the returns of the skew and smile trades cannot be explained by the CAPM.