On the Implied Volatility Skew Outside the At-the-Money Point

17 Pages Posted: 23 May 2023 Last revised: 3 Jul 2023

See all articles by Michele Azzone

Michele Azzone

Polytechnic University of Milan - Department of Mathematics

Lorenzo Torricelli

University of Bologna Department of Statistics

Date Written: May 19, 2023

Abstract

The small-maturity implied volatility of an asset pricing model is fully determined by the asymptotics of traded option prices, and thus model-free expressions are available. We show how by sharpening one such expression it is possible to derive a general formula for the leading order of the in-the-money and out-of the money implied volatility skew. We apply this to the Heston model, exponential Lévy models and their time changes, as well as to some recently proposed pricing models with independent returns increments.

Keywords: Implied volatility, out-of-the-money implied volatility skew

JEL Classification: 91G20

Suggested Citation

Azzone, Michele and Torricelli, Lorenzo, On the Implied Volatility Skew Outside the At-the-Money Point (May 19, 2023). Available at SSRN: https://ssrn.com/abstract=4453112 or http://dx.doi.org/10.2139/ssrn.4453112

Michele Azzone

Polytechnic University of Milan - Department of Mathematics ( email )

Via Bonardi, 9
Milano, MI 20133
Italy

Lorenzo Torricelli (Contact Author)

University of Bologna Department of Statistics ( email )

Via Belle Arti
Bologna, 40121
Italy

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