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Path-dependent volatility and the preservation of PDEs
Dissertation (MSc)--University of Pretoria, 2016.
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| Other Authors: | |
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2017
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| _version_ | 1867613454679932928 |
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| access_status_str | Open Access |
| author2 | Van Zyl, A.J. |
| author_browse | Van Zyl, A.J. |
| author_facet | Van Zyl, A.J. |
| collection | Thesis |
| dc_rights_str_mv | © 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. |
| description | Dissertation (MSc)--University of Pretoria, 2016. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/60823 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:24.683Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/60823 Path-dependent volatility and the preservation of PDEs Van Zyl, A.J. michaellight22@gmail.com Light, Michael UCTD Dissertation (MSc)--University of Pretoria, 2016. The 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. Mathematics and Applied Mathematics MSc Unrestricted 2017-06-05T12:11:01Z 2017-06-05T12:11:01Z 2017-04-21 2016 Dissertation Light, M 2016, Path-dependent volatility and the preservation of PDEs, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/60823> A2017 http://hdl.handle.net/2263/60823 en © 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. application/pdf University of Pretoria |
| spellingShingle | UCTD Path-dependent volatility and the preservation of PDEs |
| title | Path-dependent volatility and the preservation of PDEs |
| title_full | Path-dependent volatility and the preservation of PDEs |
| title_fullStr | Path-dependent volatility and the preservation of PDEs |
| title_full_unstemmed | Path-dependent volatility and the preservation of PDEs |
| title_short | Path-dependent volatility and the preservation of PDEs |
| title_sort | path dependent volatility and the preservation of pdes |
| topic | UCTD |
| url | http://hdl.handle.net/2263/60823 |