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dc.contributor.authorElie, Romuald*
dc.contributor.authorLépinette, Emmanuel*
dc.date.accessioned2016-02-09T09:08:51Z
dc.date.available2016-02-09T09:08:51Z
dc.date.issued2015
dc.identifier.issn0949-2984
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/15349
dc.language.isoenen
dc.subjectLeland–Lott strategyen
dc.subjectDelta hedgingen
dc.subjectMalliavin calculusen
dc.subjectTransaction costsen
dc.subjectOrder booken
dc.subject.classificationjelG.G1.G13en
dc.subject.classificationjelG.G1.G11en
dc.titleApproximate hedging for nonlinear transaction costs on the volume of traded assetsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is dedicated to the replication of a convex contingent claim h(S 1) in a financial market with frictions, due to deterministic order books or regulatory constraints. The corresponding transaction costs can be rewritten as a nonlinear function G of the volume of traded assets, with G′(0)>0. For a stock with Black–Scholes midprice dynamics, we exhibit an asymptotically convergent replicating portfolio, defined on a regular time grid with n trading dates. Up to a well-chosen regularization h n of the payoff function, we first introduce the frictionless replicating portfolio of hn(Sn1), where S n is a fictitious stock with enlarged local volatility dynamics. In the market with frictions, a suitable modification of this portfolio strategy provides a terminal wealth that converges in L2 to the claim h(S 1) as n goes to infinity. In terms of order book shapes, the exhibited replicating strategy only depends on the size 2G′(0) of the bid–ask spread. The main innovation of the paper is the introduction of a “Leland-type” strategy for nonvanishing (nonlinear) transaction costs on the volume of traded shares, instead of the commonly considered traded amount of money. This induces lots of technicalities, which we overcome by using an innovative approach based on the Malliavin calculus representation of the Greeks.en
dc.relation.isversionofjnlnameFinance and Stochastics
dc.relation.isversionofjnlvol19en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages541-581en
dc.relation.isversionofdoi10.1007/s00780-015-0262-2en
dc.relation.isversionofjnlpublisherSpringeren
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-02-09T08:58:11Z
hal.person.labIds29*
hal.person.labIds60*
hal.identifierhal-01271354*


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