What Does Implied Volatility Skew Measure?

Abstract

The Black–Scholes model has been acknowledged as a brilliant breakthrough in asset pricing theory. But in applying it to real world options, problems immediately arose, because the volatility that make an option’s model value consistent with its market price is different for different strike prices: the wellknown “volatility smile.” Over time, the smile evolved into a more monotonic, downward-sloping “skew,” and traders became comfortable with the idea of modeling its behavior and describing option market conditions in terms of the level and skew of implied volatilities. A standard explanation for the skew is that the return distribution is not lognormal; in particular, it generally has a negative third moment (i.e., negative skewness). The similarity of the terms and the (potential) connection between the volatility skew and statistical skewness is one source of confusion. Another is that (unlike skewness) there is no standard measure for the volatility skew. Mixon explores these issues and reviews a number of common skew measures. One significant result is that most of them vary strongly with the level of volatility, making comparisons across different underlying assets or over time difficult. After examining several performance measures, Mixon suggests that the most useful measure of the volatility skew is the difference between the implied volatilities for a 25 delta put and a 25 delta call, divided by the implied volatility for a 50 delta option.