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Modelling Equities with a Stochastic Volatility Jump Diffusion
The Bates model provides a parsimonious fit to implied volatility surfaces, and its usefulness in developed markets is well documented. However, there is a lack of research assessing its applicability to developing markets. Additionally, research surrounding its usefulness for hedging long term liab...
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| Format: | Thesis |
| Language: | English |
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African Institute of Financial Markets and Risk Management
2019
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| _version_ | 1867613274700251136 |
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| access_status_str | Open Access |
| author | Gorven, Matthew |
| author2 | Mahomed, Obeid |
| author_browse | Gorven, Matthew Mahomed, Obeid |
| author_facet | Mahomed, Obeid Gorven, Matthew |
| author_sort | Gorven, Matthew |
| collection | Thesis |
| description | The Bates model provides a parsimonious fit to implied volatility surfaces, and its usefulness in developed markets is well documented. However, there is a lack of research assessing its applicability to developing markets. Additionally, research surrounding its usefulness for hedging long term liabilities is limited, despite its frequent use for this purpose. This dissertation dissects the dynamics of the Bates model into the Heston and Merton models in order to separately examine the effects of stochastic volatility and jumps. Challenges surrounding application of this model are investigated through an evaluation of risk-neutral calibration and simulation methods. The model’s ability to fit the implied volatility surfaces from the JSE Top 40 equity index is analysed. Lastly, an evaluation of the model’s delta and vega hedging performance is presented by comparing it to the hedge performance of other commonly used models. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/29448 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:31.121Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | African Institute of Financial Markets and Risk Management |
| publisherStr | African Institute of Financial Markets and Risk Management |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/29448 Modelling Equities with a Stochastic Volatility Jump Diffusion Gorven, Matthew Mahomed, Obeid Taylor, David Mathematical Finance The Bates model provides a parsimonious fit to implied volatility surfaces, and its usefulness in developed markets is well documented. However, there is a lack of research assessing its applicability to developing markets. Additionally, research surrounding its usefulness for hedging long term liabilities is limited, despite its frequent use for this purpose. This dissertation dissects the dynamics of the Bates model into the Heston and Merton models in order to separately examine the effects of stochastic volatility and jumps. Challenges surrounding application of this model are investigated through an evaluation of risk-neutral calibration and simulation methods. The model’s ability to fit the implied volatility surfaces from the JSE Top 40 equity index is analysed. Lastly, an evaluation of the model’s delta and vega hedging performance is presented by comparing it to the hedge performance of other commonly used models. 2019-02-08T14:19:31Z 2019-02-08T14:19:31Z 2018 2019-02-07T07:19:34Z Master Thesis Masters MPhil http://hdl.handle.net/11427/29448 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Gorven, Matthew Modelling Equities with a Stochastic Volatility Jump Diffusion |
| thesis_degree_str | Master's |
| title | Modelling Equities with a Stochastic Volatility Jump Diffusion |
| title_full | Modelling Equities with a Stochastic Volatility Jump Diffusion |
| title_fullStr | Modelling Equities with a Stochastic Volatility Jump Diffusion |
| title_full_unstemmed | Modelling Equities with a Stochastic Volatility Jump Diffusion |
| title_short | Modelling Equities with a Stochastic Volatility Jump Diffusion |
| title_sort | modelling equities with a stochastic volatility jump diffusion |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/29448 |
| work_keys_str_mv | AT gorvenmatthew modellingequitieswithastochasticvolatilityjumpdiffusion |