Fixed domain transformations and split-step finite difference schemes for Nonlinear Black-Scholes equations for American Options

dc.contributor.authorAnkudinova, Julia
dc.contributor.authorEhrhardt, Matthias
dc.date.accessioned2022-05-11T12:11:41Z
dc.date.available2022-05-11T12:11:41Z
dc.date.issued2008-02-20
dc.description.abstractDue to transaction costs, illiquid markets, large investors or risks from an unprotected portfolio the assumptions in the classical Black-Scholes model become unrealistic and the model results in strongly or fully nonlinear, possibly degenerate, parabolic diffusion-convection equations, where the stock price, volatility, trend and option price may depend on the time, the stock price or the option price itself. In this chapter we will be concerned with several models from the most relevant class of nonlinear Black-Scholes equations for American options with a volatility depending on different factors, such as the stock price, the time, the option price and its derivatives. We will analytically approach the option price by following the ideas proposed by Ševčovič and transforming the free boundary problem into a fully nonlinear nonlocal parabolic equation defined on a fixed, but unbounded domain. Finally, we will present the results of a split-step finite difference schemes for various volatility models including the Leland model, the Barles and Soner model and the Risk adjusted pricing methodology model.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/16896
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-15674
dc.language.isoen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematiken
dc.subject.othernonlinear Black-Scholes modelsen
dc.subject.otherfixed domain transformationen
dc.subject.othersplit-step methodsen
dc.subject.otherAmerican optionsen
dc.titleFixed domain transformations and split-step finite difference schemes for Nonlinear Black-Scholes equations for American Optionsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2008, 07en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200035A35 Theoretical approximation to solutionsen
tub.subject.msc200065N99 None of the above, but in this sectionen
tub.subject.msc200091B26 Market modelsen
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