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Lévy Processes in Finance
The Change of Measure and Non-Linear Dependence

dc.contributor.advisorSandmann, Klaus
dc.contributor.authorWannenwetsch, Jens
dc.date.accessioned2020-04-07T21:58:10Z
dc.date.available2020-04-07T21:58:10Z
dc.date.issued2005
dc.identifier.urihttp://hdl.handle.net/20.500.11811/2252
dc.description.abstractThis thesis deals with applications of Lévy processes in the field of mathematical finance. The class of Lévy processes generalizes the widely used Brownian motion in the sense that the distribution of their increments can model the statistically observed heavy-tailed and skewed returns of a broad range of exchange-traded assets.
The problem of the incompleteness of a Lévy driven market is dealt with in the first part. Incompleteness leads to non-uniqueness of the martingale measure and hence to the problem of selecting a specific one. Two different solutions are proposed: The first is an ad hoc change of measure based on qualitative economic considerations whereas the second gives a simple method of how to fit a carefully chosen family of martingale measures to observed option prices.
While the first part has focused on scalar modelling issues, the second one is concerned about multidimensional Lévy processes. A two-dimensional asset price model is proposed where the marginal distributions incorporate heavy tails and skewness and, in addition, the dependence between the two assets is modeled by a mixture of the well-known linear dependence and a computationally tractable form of tail dependence. For this model a method of approximating prices of basket options is proposed and compared to a fast Monte Carlo method as well as to prices obtained in the standard two-dimensional diffusion model. Finally, it is shown how hedging of multidimensional options can be done in a Lévy model.
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectLevyprozesse
dc.subjectUnvollständigkeit
dc.subjectOptionsbewertung
dc.subjectIndexoptionen
dc.subjectMasswechsel
dc.subjectCopula
dc.subjectrisikoneutral
dc.subjectIncompleteness
dc.subjectoption pricing
dc.subjectbasket options
dc.subjectmeasure change
dc.subjectrisk-neutral
dc.subject.ddc330 Wirtschaft
dc.titleLévy Processes in Finance
dc.title.alternativeThe Change of Measure and Non-Linear Dependence
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5-05459
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID545
ulbbnediss.date.accepted2005-06-17
ulbbnediss.fakultaetRechts- und Staatswissenschaftliche Fakultät
dc.contributor.coRefereeSchürger, Klaus


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