Defining Skew for a Volatility Smile and Choosing Moneyness Points

Summary

The document raises two related questions about volatility smile terminology. First, it asks whether skew has a generally accepted definition and whether it means the derivative of implied volatility with respect to strike, with maturity held as an argument of the implied volatility surface. Second, it asks whether practitioners typically focus on at-the-money-forward skew or also examine other strikes or moneyness points.

No answers, conventions, formulas beyond the proposed strike derivative, or market examples are included. Consequently, the text does not establish that strike sensitivity is the universal definition, nor does it describe how skew may be measured using delta or another moneyness coordinate. It also provides no evidence about common practice across asset classes or applications. The document is best treated as a terminology question that highlights the need to specify the coordinate, maturity, and point or region of the smile when discussing skew; it does not support a definitive convention or recommendation.

Key ideas

• The document asks whether volatility skew means the implied volatility derivative with respect to strike.
• It distinguishes the question of definition from the choice of coordinate used to describe the smile.
• It asks whether at-the-money-forward skew is the usual focus or whether other points are analyzed.
• No answer or market evidence is provided, so no standard convention is established.

Tags

# Terminology : definition of skew for a volatility smile


# Terminology : definition of skew for a volatility smile












Is there a generally accepted definition of skew for volatility smiles? Is skew always defined as $$ \frac{\partial{\widehat{\sigma}(K,T)}}{\partial{K}}, $$ where $\hat{\sigma}:[0;+\infty)\times[0;+\infty)\to[0;+\infty)$ is the implied volatility surface ?

Is it typical to work with ATMF skew and not look at other strikes/moneyness points?

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