On the skew and curvature of the implied and local volatilities
Mostra el registre complet Registre parcial de l'ítem
- dc.contributor.author Alòs, Elisa
- dc.contributor.author García-Lorite, David
- dc.contributor.author Pravosud, Makar
- dc.date.accessioned 2024-02-19T07:24:48Z
- dc.date.embargoEnd info:eu-repo/date/embargoEnd/2025-03-09
- dc.date.issued 2023
- dc.description.abstract In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent 1H+3/2 rule (where H denotes the Hurst parameter of the volatility process) for rough volatilities (see F. Bourgey, S. De Marco, P. Friz, and P. Pigato. 2022. “Local Volatility under Rough Volatility.” arXiv:2204.02376v1 [q-fin.MF] https://doi.org/10.48550/arXiv.2204.02376.), that states that the short-time skew slope of the at-the-money implied volatility is 1H+3/2 of the corresponding slope for local volatilities. Moreover, we see that the at-the-money short-end curvature of the implied volatility can be written in terms of the short-end skew and curvature of the local volatility and vice versa. Additionally, this relationship depends on H.
- dc.embargo.liftdate 2025-03-09
- dc.format.mimetype application/pdf
- dc.identifier.citation Alòs E, García-Lorite D, Pravosud M. On the skew and curvature of the implied and local volatilities. Appl Math Finance. 2023;30(1):47-67. DOI: 10.1080/1350486X.2023.2261459
- dc.identifier.doi http://dx.doi.org/10.1080/1350486X.2023.2261459
- dc.identifier.issn 1350-486X
- dc.identifier.uri http://hdl.handle.net/10230/59131
- dc.language.iso eng
- dc.publisher Taylor & Francis
- dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/PID2020-118339GB-I00
- dc.rights © This is an Accepted Manuscript of an article published by Taylor & Francis in Applied mathematical finance on 09 Oct 2023, available online: http://www.tandfonline.com/10.1080/1350486X.2023.2261459
- dc.rights.accessRights info:eu-repo/semantics/embargoedAccess
- dc.subject.keyword Stochastic volatility
- dc.subject.keyword local volatility
- dc.subject.keyword rough volatility
- dc.subject.keyword Malliavin calculus
- dc.title On the skew and curvature of the implied and local volatilities
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/acceptedVersion