Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models

We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short...

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Detalles Bibliográficos
Autores principales: Gerhold, Stefan, Gülüm, I. Cetin, Pinter, Arpad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Routledge 2016
Materias:
Original Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5012375/
https://www.ncbi.nlm.nih.gov/pubmed/27660537
http://dx.doi.org/10.1080/1350486X.2016.1197041
Descripción
Sumario:We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee’s moment formula.

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