What is the implied volatility skew?

  • I often hear people talking about the skew of the volatility surface, model, etc... but it appears to me that a clear standard definition is not unanimously in place among practitioners.

    So here is my question: Does anyone has a clear and unifying definition that can be stated in mathematical terms of what skew is in the context of risk neutral pricing? If not, do you have a set of definitions of the skew with respect to a specific context?

    Given that I found an entire paper in the JOD devoted to this question, I think it is arguably not "soft," so I removed that tag. Skew is also a technical term, not "jargon", so I removed that tag, too.

  • Scott Mixon argues in What Does Implied Volatility Skew Measure that among all measures of implied volatility skew, the (25 delta put volatility - 25 delta call volatility)/50 delta volatility is the most descriptive and least redundant (volatility is Black-Scholes implied volatility). His paper, recently published in the Journal of Derivatives, gives a number of both theoretical and empirical arguments in favor of this measure. He distinguishes between "skew", which is a measure of the slope of the implied volatility curve for a given expiration date, and "skewness", which is the skewness of an option implied, risk neutral probability distribution. To calculate the latter, one needs to have a theoretical framework or model, whereas the former is easily observable from options prices.

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Content dated before 7/24/2021 11:53 AM