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
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author Gerhold, Stefan
Gülüm, I. Cetin
Pinter, Arpad
author_facet Gerhold, Stefan
Gülüm, I. Cetin
Pinter, Arpad
author_sort Gerhold, Stefan
collection PubMed
description 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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spelling pubmed-50123752016-09-20 Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models Gerhold, Stefan Gülüm, I. Cetin Pinter, Arpad Appl Math Finance Original Articles 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. Routledge 2016-03-03 2016-06-30 /pmc/articles/PMC5012375/ /pubmed/27660537 http://dx.doi.org/10.1080/1350486X.2016.1197041 Text en © 2016 The Author(s). published by Informa UK Limited, trading as Taylor & Francis Group http://creativecommons.org/licenses/by/4.0/ This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Original Articles
Gerhold, Stefan
Gülüm, I. Cetin
Pinter, Arpad
Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models
title Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models
title_full Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models
title_fullStr Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models
title_full_unstemmed Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models
title_short Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models
title_sort small-maturity asymptotics for the at-the-money implied volatility slope in lévy models
topic Original Articles
url 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
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