What Does Implied Volatility Skew Measure?

This article provides theoretical guidance and empirical analysis aimed at differentiating among implied volatility skew measures. Industry analysts and academics use a variety of measures, but most have little formal justification. The author finds that most commonly used skew measures are difficult to interpret without controlling for the levels of both volatility and kurtosis. Many ad hoc measures fail to meet the conditions for a valid skewness ordering. The author's preferred measure is the (25 delta put volatility-25 delta call volatility)/50 delta volatility; among the measures considered, it is the most descriptive and least redundant.