On the implied volatility of Inverse options under stochastic volatility models

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• dc.contributor.author Alòs, Elisa
• dc.contributor.author Nualart, Eulàlia
• dc.contributor.author Pravosud, Makar
• dc.date.accessioned 2025-06-05T12:15:31Z
• dc.date.available 2025-06-05T12:15:31Z
• dc.date.issued 2025
• dc.date.updated 2025-06-05T12:15:31Z
• dc.description Data de publicació electrònica: 13-05-2025
• dc.description.abstract In 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.
• dc.description.sponsorship EN acknowledges support from the Spanish MINECO grant PID2022-138268NB-100 and Ayudas Fundacion BBVA a Equipos de Investigación Científica 2021.
• dc.format.mimetype application/pdf
• dc.identifier.citation Alòs E, Nualart E, Pravosud M. On the implied volatility of Inverse options under stochastic volatility models. Decis. Econ. Finance. 2025 May 13. DOI: 10.1007/s10203-025-00522-z
• dc.identifier.doi http://dx.doi.org/10.1007/s10203-025-00522-z
• dc.identifier.issn 1593-8883
• dc.identifier.uri http://hdl.handle.net/10230/70625
• dc.language.iso eng
• dc.publisher Springer
• dc.relation.ispartof Decisions in Economics and Finance. 2025 May 13
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PE/PID2022-138268NB-100
• dc.rights This 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/.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Inverse European options
• dc.subject.keyword Stochastic volatility
• dc.subject.keyword Crypto derivatives
• dc.subject.keyword Malliavin calculus
• dc.subject.keyword Implied volatility
• dc.title On the implied volatility of Inverse options under stochastic volatility models
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion