Summarizing Equity Volatility Skews with Level, Slope, and Curvature

Summary

The document asks how volatility quants describe the shape of an equity options implied volatility skew using statistics beyond basic distribution summaries. It groups candidate features into level, represented by at-the-money implied volatility; skew, represented by risk reversal and butterfly spreads; and curvature, potentially captured through ratios comparing off-ATM implied volatilities with the ATM value. A collection of such ratios could describe the shape across strikes more fully than a single skew measure.

The author also asks whether SVI-JW is a suitable model for fitting an equity volatility skew, noting that the cited work applies it to SPX options. This is a question rather than a tested conclusion: no dataset, comparison of fit quality, or validation evidence is presented. The document is useful as a framing of candidate summary dimensions, but it does not establish industry standards or show that a model that fits SPX will fit other equity options well.

Key ideas

• ATM implied volatility can summarize the level of a volatility skew.
• Risk reversals and butterfly spreads are candidate measures of skew and curvature.
• Ratios of off-ATM to ATM implied volatility can describe shape across multiple strikes.
• The author asks whether SVI-JW fits equity skews, but presents no empirical test or conclusion.

Tags

# Are there standardized measures to characterize the volatility skew?


# Are there standardized measures to characterize the volatility skew?












Might be too simple a question, but I saw in Gatheral & Jacquier (2014) that commonly used features to match volatility skews are (and then I subsequently ChatGPTed some commonly used industry metrics):

- Level - such as the ATM IV

- Skew - such as the RR and Butterfly Spreads

- Curvature - such as the "Volatility Ratio", which refers to the ratio of IV of other options relative to the ATM IV. I guess the point of this ratio is to look at multiple ratios to analyze the how curved the whole skew is, which is a step up from the RR.

My question is, are there standardized metrics used by volatility quants in the industry? I am currently working with an equity volatility skew and wanted to get some useful summary statistics to analyze my dataset (beyond the simple mean, SD, kurtosis, upper/lower quantiles etc.).

Also, a more specific question would be to probably analyze if the SVI-JW is a good fit for fitting my equity volatility skew. However, since Gatheral & Jacquier (2014) do fit their methodology to SPX options, I would expect that the SVI-JW method is a naturally good choice.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.