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dc.date.accessioned2017-03-28T10:58:16Z
dc.date.available2018-01-04T23:31:40Z
dc.date.created2016-11-11T18:40:15Z
dc.date.issued2017
dc.identifier.citationBaños, David Ruiz Meyer-Brandis, Thilo Proske, Frank Norbert Duedahl, Sindre . Computing Deltas without Derivatives. Finance and Stochastics. 2017
dc.identifier.urihttp://hdl.handle.net/10852/55124
dc.description.abstractA well-known application of Malliavin calculus in mathematical finance is the probabilistic representation of option price sensitivities, the so-called Greeks, as expectation functionals that do not involve the derivative of the payoff function. This allows numerically tractable computation of the Greeks even for discontinuous payoff functions. However, while the payoff function is allowed to be irregular, the coefficients of the underlying diffusion are required to be smooth in the existing literature, which for example already excludes simple regime-switching diffusion models. The aim of this article is to generalise this application of Malliavin calculus to Itô diffusions with irregular drift coefficients, where we focus here on the computation of the delta, which is the option price sensitivity with respect to the initial value of the underlying. To this end, we first show existence, Malliavin differentiability and (Sobolev) differentiability in the initial condition for strong solutions of Itô diffusions with drift coefficients that can be decomposed into the sum of a bounded, but merely measurable, and a Lipschitz part. Furthermore, we give explicit expressions for the corresponding Malliavin and Sobolev derivatives in terms of the local time of the diffusion, respectively. We then turn to the main objective of this article and analyse the existence and probabilistic representation of the corresponding deltas for European and path-dependent options. We conclude with a small simulation study of several regime-switching examples. The final version of this research has been published by Finance and Stochastics. © Springer Verlag.en_US
dc.languageEN
dc.publisherSpringer Berlin/Heidelberg
dc.titleComputing Deltas without Derivativesen_US
dc.typeJournal articleen_US
dc.creator.authorBaños, David Ruiz
dc.creator.authorMeyer-Brandis, Thilo
dc.creator.authorProske, Frank Norbert
dc.creator.authorDuedahl, Sindre
cristin.unitcode185,15,13,35
cristin.unitnameStokastisk analyse, finans, forsikring og risiko
cristin.ispublishedtrue
cristin.fulltextoriginal
cristin.qualitycode1
dc.identifier.cristin1399704
dc.identifier.bibliographiccitationinfo:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Finance and Stochastics&rft.volume=&rft.spage=&rft.date=2017
dc.identifier.jtitleFinance and Stochastics
dc.identifier.volume21
dc.identifier.issue2
dc.identifier.startpage509
dc.identifier.endpage549
dc.identifier.doihttp://dx.doi.org/10.1007/s00780-016-0321-3
dc.identifier.urnURN:NBN:no-57932
dc.type.documentTidsskriftartikkelen_US
dc.type.peerreviewedPeer reviewed
dc.source.issn0949-2984
dc.identifier.fulltextFulltext https://www.duo.uio.no/bitstream/handle/10852/55124/4/DeltasAcceptedRevised.pdf
dc.type.versionAcceptedVersion


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