Path-dependent volatility and the preservation of PDEs

dc.contributor.advisorVan Zyl, A.J.en
dc.contributor.emailmichaellight22@gmail.comen
dc.contributor.postgraduateLight, Michaelen
dc.date.accessioned2017-06-05T12:11:01Z
dc.date.available2017-06-05T12:11:01Z
dc.date.created2017-04-21en
dc.date.issued2016en
dc.descriptionDissertation (MSc)--University of Pretoria, 2016.en
dc.description.abstractThe classical theory of risk neutral derivative pricing relies on the underlying market model being Markovian and complete. We present the theory of stochastic di erential equations relevant to risk neutral pricing, with a particular focus on the Markov property and its links to partial di erential equations. We demonstrate when this classical theory can still be applied to derivative pricing in models with path dependent volatility. A link between these models and the local volatility framework is derived via the representation of local volatility as the conditional expectation of some, more complicated, process. Julien Guyon used this link as a tool in tting a large class of models to the market. We will propose a tted, complete and Markovian market model, which incorporates past asset levels in future volatility levels. The numerical implementation of such a model is addressed through a Monte Carlo scheme incorporating Guyon's particle method, as well as a nite difference scheme.en_ZA
dc.description.availabilityUnrestricteden
dc.description.degreeMScen
dc.description.departmentMathematics and Applied Mathematicsen
dc.identifier.citationLight, M 2016, Path-dependent volatility and the preservation of PDEs, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/60823>en
dc.identifier.otherA2017en
dc.identifier.urihttp://hdl.handle.net/2263/60823
dc.language.isoenen
dc.publisherUniversity of Pretoriaen
dc.rights© 2017 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.en
dc.subjectUCTDen
dc.titlePath-dependent volatility and the preservation of PDEsen
dc.typeDissertationen

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