On smile properties of volatility derivatives: understanding the VIX skew

We develop a method to study the implied volatility of exotic underlyings, with special focus on volatility derivatives such as VIX options. Remarkably, our approach is flexible enough to be applied to any underlying, subject to mild technical conditions. Our method, built upon Malliavin calculus te...

Descripción completa

Detalles Bibliográficos
Autores: Alòs, Elisa, García-Lorite, David, Muguruza Gonzalez, Aitor
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/59132
Acceso en línea:http://hdl.handle.net/10230/59132
http://dx.doi.org/10.1137/19M1269981
Access Level:acceso abierto
Palabra clave:variance options
VIX
implied volatility
Malliavin calculus
stochastic volatility models
rough volatility
fractional Brownian motion
id ES_e48d3e3c4e8b35841fa1cece6556e874
oai_identifier_str oai:recercat.cat:10230/59132
network_acronym_str ES
network_name_str España
repository_id_str
spelling On smile properties of volatility derivatives: understanding the VIX skewAlòs, ElisaGarcía-Lorite, DavidMuguruza Gonzalez, Aitorvariance optionsVIXimplied volatilityMalliavin calculusstochastic volatility modelsrough volatilityfractional Brownian motionWe develop a method to study the implied volatility of exotic underlyings, with special focus on volatility derivatives such as VIX options. Remarkably, our approach is flexible enough to be applied to any underlying, subject to mild technical conditions. Our method, built upon Malliavin calculus techniques, allows to transform any such underlying into the Black--Scholes model with a particular type of stochastic volatility. This, in turn, allows us to describe the properties of the at-the-money implied volatility (ATMI) in terms of the Malliavin derivatives of the transformed underlying process. Concretely, we study the short-time behavior of the ATMI level and skew. As an application, we describe the short-term behavior of the ATMI of VIX and realize variance options in terms of the Hurst parameter of the model, and most importantly, we describe the class of volatility processes that generate a positive skew for the VIX implied volatility. Several numerical examples are provided to support our theoretical results.SIAM (Society for Industrial and Applied Mathematics)202420242022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/59132http://dx.doi.org/10.1137/19M1269981reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésJournal on Financial Mathematics. 2022;13(1):35 p.© 2022 by SIAM. Unauthorized reproduction of this article is prohibited. First Published in SIAM Journal on Financial Mathematics in 13,1, published by the Society for Industrial and Applied Mathematics (SIAM).info:eu-repo/semantics/openAccessoai:recercat.cat:10230/591322026-05-29T05:05:01Z
dc.title.none.fl_str_mv On smile properties of volatility derivatives: understanding the VIX skew
title On smile properties of volatility derivatives: understanding the VIX skew
spellingShingle On smile properties of volatility derivatives: understanding the VIX skew
Alòs, Elisa
variance options
VIX
implied volatility
Malliavin calculus
stochastic volatility models
rough volatility
fractional Brownian motion
title_short On smile properties of volatility derivatives: understanding the VIX skew
title_full On smile properties of volatility derivatives: understanding the VIX skew
title_fullStr On smile properties of volatility derivatives: understanding the VIX skew
title_full_unstemmed On smile properties of volatility derivatives: understanding the VIX skew
title_sort On smile properties of volatility derivatives: understanding the VIX skew
dc.creator.none.fl_str_mv Alòs, Elisa
García-Lorite, David
Muguruza Gonzalez, Aitor
author Alòs, Elisa
author_facet Alòs, Elisa
García-Lorite, David
Muguruza Gonzalez, Aitor
author_role author
author2 García-Lorite, David
Muguruza Gonzalez, Aitor
author2_role author
author
dc.subject.none.fl_str_mv variance options
VIX
implied volatility
Malliavin calculus
stochastic volatility models
rough volatility
fractional Brownian motion
topic variance options
VIX
implied volatility
Malliavin calculus
stochastic volatility models
rough volatility
fractional Brownian motion
description We develop a method to study the implied volatility of exotic underlyings, with special focus on volatility derivatives such as VIX options. Remarkably, our approach is flexible enough to be applied to any underlying, subject to mild technical conditions. Our method, built upon Malliavin calculus techniques, allows to transform any such underlying into the Black--Scholes model with a particular type of stochastic volatility. This, in turn, allows us to describe the properties of the at-the-money implied volatility (ATMI) in terms of the Malliavin derivatives of the transformed underlying process. Concretely, we study the short-time behavior of the ATMI level and skew. As an application, we describe the short-term behavior of the ATMI of VIX and realize variance options in terms of the Hurst parameter of the model, and most importantly, we describe the class of volatility processes that generate a positive skew for the VIX implied volatility. Several numerical examples are provided to support our theoretical results.
publishDate 2022
dc.date.none.fl_str_mv 2022
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/59132
http://dx.doi.org/10.1137/19M1269981
url http://hdl.handle.net/10230/59132
http://dx.doi.org/10.1137/19M1269981
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal on Financial Mathematics. 2022;13(1):35 p.
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv SIAM (Society for Industrial and Applied Mathematics)
publisher.none.fl_str_mv SIAM (Society for Industrial and Applied Mathematics)
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869422601048162304
score 15,81155

Similares en LA Referencia