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arXiv · 1310.3061

Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models

Stefan Gerhold·I. Cetin Gülüm·Arpad Pinter
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Abstract

We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity at-the-money digital call options, using Mellin transform asymptotics. Finally, we discuss when the at-the-money slope is consistent with the steepness of the smile wings, as given by Lee's moment formula.

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Stefan Gerhold, I. Cetin Gülüm, Arpad Pinter. 2016-05-30. Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models. https://arxiv.org/abs/1310.3061

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