On the optimal choice of strike conventions in exchange option pricing

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• dc.contributor.author Alòs, Elisa
• dc.contributor.author Coulon, Michael
• dc.date.accessioned 2025-06-10T14:41:56Z
• dc.date.available 2025-06-10T14:41:56Z
• dc.date.issued 2024
• dc.date.updated 2025-06-10T14:41:55Z
• dc.description.abstract An important but rarely-addressed option pricing question is how to choose appropriate strikes for implied volatility inputs when pricing more exotic multi-asset derivatives. By means of Malliavin calculus, we construct an asymptotically optimal log-linear strike convention for exchange options under stochastic volatility models. This novel approach allows us to minimize the difference between the corresponding Margrabe computed price and the true option price. We show that this optimal convention does not depend on the specific stochastic volatility model chosen and, furthermore, that parameter estimation can be dramatically simplified by using market observables as inputs. Numerical examples are given that provide strong support for the new methodology.
• dc.description.sponsorship This research was funded by the Ministerio de Ciencia e Innovación (Spain), grant number PID2020-118339GB.
• dc.format.mimetype application/pdf
• dc.identifier.citation Alòs E, Coulon M. On the optimal choice of strike conventions in exchange option pricing. Mathematics. 2024;12(19):3028. DOI: 10.3390/math12193028
• dc.identifier.doi http://dx.doi.org/10.3390/math12193028
• dc.identifier.issn 2227-7390
• dc.identifier.uri http://hdl.handle.net/10230/70654
• dc.language.iso eng
• dc.publisher MDPI
• dc.relation.ispartof Mathematics. 2024;12(19): 3028
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/PID2020-118339GB
• dc.rights © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://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 Exchange option
• dc.subject.keyword Implied volatility
• dc.subject.keyword Margrabe formula
• dc.subject.keyword Malliavin calculus
• dc.title On the optimal choice of strike conventions in exchange option pricing
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion