On the implied volatility of Inverse options under stochastic volatility models

Data de publicació electrònica: 13-05-2025

Detalles Bibliográficos
Autores: Alòs, Elisa, Nualart, Eulàlia, Pravosud, Makar
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
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:10230/70625
Acceso en línea:http://hdl.handle.net/10230/70625
http://dx.doi.org/10.1007/s10203-025-00522-z
Access Level:acceso abierto
Palabra clave:Inverse European options
Stochastic volatility
Crypto derivatives
Malliavin calculus
Implied volatility
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spelling On the implied volatility of Inverse options under stochastic volatility modelsAlòs, ElisaNualart, EulàliaPravosud, MakarInverse European optionsStochastic volatilityCrypto derivativesMalliavin calculusImplied volatilityData de publicació electrònica: 13-05-2025In this paper, we study the short-time behavior of at-the-money implied volatility for inverse European options with a fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques from Malliavin calculus, such as the anticipating Itô's formula, we first compute the implied volatility of the option as its maturity approaches zero. Next, we derive a short-maturity asymptotic formula for the skew of the implied volatility, which depends on the roughness of the volatility model. We also demonstrate that our results can be easily extended to Quanto-Inverse options. We apply our general findings to the SABR and fractional Bergomi models and provide numerical simulations that confirm the accuracy of the asymptotic formula for the skew. Finally, we present an empirical application using Bitcoin options traded on Deribit, showing how our theoretical formulas can be applied to model real market data for such options.EN acknowledges support from the Spanish MINECO grant PID2022-138268NB-100 and Ayudas Fundacion BBVA a Equipos de Investigación Científica 2021.Springer2025202520252025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/70625http://dx.doi.org/10.1007/s10203-025-00522-zhttp://hdl.handle.net/10230/70625reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésDecisions in Economics and Finance. 2025 May 13info:eu-repo/grantAgreement/ES/3PE/PID2022-138268NB-100This article is licensed under a CreativeCommonsAttribution 4.0 InternationalLicense, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:10230/706252026-05-29T05:05:01Z
dc.title.none.fl_str_mv On the implied volatility of Inverse options under stochastic volatility models
title On the implied volatility of Inverse options under stochastic volatility models
spellingShingle On the implied volatility of Inverse options under stochastic volatility models
Alòs, Elisa
Inverse European options
Stochastic volatility
Crypto derivatives
Malliavin calculus
Implied volatility
title_short On the implied volatility of Inverse options under stochastic volatility models
title_full On the implied volatility of Inverse options under stochastic volatility models
title_fullStr On the implied volatility of Inverse options under stochastic volatility models
title_full_unstemmed On the implied volatility of Inverse options under stochastic volatility models
title_sort On the implied volatility of Inverse options under stochastic volatility models
dc.creator.none.fl_str_mv Alòs, Elisa
Nualart, Eulàlia
Pravosud, Makar
author Alòs, Elisa
author_facet Alòs, Elisa
Nualart, Eulàlia
Pravosud, Makar
author_role author
author2 Nualart, Eulàlia
Pravosud, Makar
author2_role author
author
dc.subject.none.fl_str_mv Inverse European options
Stochastic volatility
Crypto derivatives
Malliavin calculus
Implied volatility
topic Inverse European options
Stochastic volatility
Crypto derivatives
Malliavin calculus
Implied volatility
description Data de publicació electrònica: 13-05-2025
publishDate 2025
dc.date.none.fl_str_mv 2025
2025
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/70625
http://dx.doi.org/10.1007/s10203-025-00522-z
http://hdl.handle.net/10230/70625
url http://hdl.handle.net/10230/70625
http://dx.doi.org/10.1007/s10203-025-00522-z
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Decisions in Economics and Finance. 2025 May 13
info:eu-repo/grantAgreement/ES/3PE/PID2022-138268NB-100
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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
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score 15,811543

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