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dc.contributor.authorTehranchi, Michael R.
dc.date.accessioned2020-10-17T15:11:11Z
dc.date.available2020-10-17T15:11:11Z
dc.date.issued2019-10-18
dc.date.submitted2017-01-27
dc.identifier.issn0949-2984
dc.identifier.others00780-019-00410-6
dc.identifier.other410
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/311640
dc.description.abstractAbstract: The space of call price curves has a natural noncommutative semigroup structure with an involution. A basic example is the Black–Scholes call price surface, from which an interesting inequality for Black–Scholes implied volatility is derived. The binary operation is compatible with the convex order, and therefore a one-parameter sub-semigroup gives rise to an arbitrage-free market model. It is shown that each such one-parameter semigroup corresponds to a unique log-concave probability density, providing a family of tractable call price surface parametrisations in the spirit of the Gatheral–Jacquier SVI surface. An explicit example is given to illustrate the idea. The key observation is an isomorphism linking an initial call price curve to the lift zonoid of the terminal price of the underlying asset.
dc.languageen
dc.publisherSpringer Berlin Heidelberg
dc.subjectArticle
dc.subjectSemigroup with involution
dc.subjectImplied volatility
dc.subjectPeacock
dc.subjectLift zonoid
dc.subjectLog-concavity
dc.subject60G44
dc.subject91G20
dc.subject60E15
dc.subject26A51
dc.subject20M20
dc.subjectD52
dc.subjectD53
dc.subjectG12
dc.titleA Black–Scholes inequality: applications and generalisations
dc.typeArticle
dc.date.updated2020-10-17T15:11:10Z
prism.endingPage38
prism.issueIdentifier1
prism.publicationNameFinance and Stochastics
prism.startingPage1
prism.volume24
dc.identifier.doi10.17863/CAM.58731
dcterms.dateAccepted2019-08-16
rioxxterms.versionofrecord10.1007/s00780-019-00410-6
rioxxterms.versionVoR
rioxxterms.licenseref.urihttps://creativecommons.org/licenses/by/4.0/
dc.identifier.eissn1432-1122


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