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Stochastic time-changed Lévy processes with their implementation
Includes bibliographical references.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Division of Actuarial Science
2015
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| _version_ | 1867613843881984000 |
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| access_status_str | Open Access |
| author | Sihlobo, Odwa |
| author2 | Mataramvura, Sure |
| author_browse | Mataramvura, Sure Sihlobo, Odwa |
| author_facet | Mataramvura, Sure Sihlobo, Odwa |
| author_sort | Sihlobo, Odwa |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/13156 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:42:35.874Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Division of Actuarial Science |
| publisherStr | Division of Actuarial Science |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/13156 Stochastic time-changed Lévy processes with their implementation Sihlobo, Odwa Mataramvura, Sure Financial Mathematics Includes bibliographical references. We focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters. 2015-06-29T07:46:30Z 2015-06-29T07:46:30Z 2014 Master Thesis Masters MPhil http://hdl.handle.net/11427/13156 eng application/pdf Division of Actuarial Science Faculty of Commerce University of Cape Town |
| spellingShingle | Financial Mathematics Sihlobo, Odwa Stochastic time-changed Lévy processes with their implementation |
| thesis_degree_str | Master's |
| title | Stochastic time-changed Lévy processes with their implementation |
| title_full | Stochastic time-changed Lévy processes with their implementation |
| title_fullStr | Stochastic time-changed Lévy processes with their implementation |
| title_full_unstemmed | Stochastic time-changed Lévy processes with their implementation |
| title_short | Stochastic time-changed Lévy processes with their implementation |
| title_sort | stochastic time changed levy processes with their implementation |
| topic | Financial Mathematics |
| url | http://hdl.handle.net/11427/13156 |
| work_keys_str_mv | AT sihloboodwa stochastictimechangedlevyprocesseswiththeirimplementation |