On the implied volatility skew outside the at-the-money point

Michele Azzone and Lorenzo Torricelli

Quantitative Finance, 2025, vol. 25, issue 1, 51-61

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 novel general formula for the leading order of the in-the-money and out-of-the money (ITM/OTM) implied volatility skew. We apply this formula to find expressions of the small maturity limiting skew of the Heston stochastic volatility model, of exponential Lévy models and their time changes, as well as that of some recently proposed pricing models with independent log returns.

Date: 2025
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DOI: 10.1080/14697688.2024.2357727

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