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Markov-Switching models and resultant equity implied volatility surfaces: a South African application
Includes bibliographical references.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867613292816498688 |
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| access_status_str | Open Access |
| author | Fairbrother, Mark |
| author2 | Becker, Ronald |
| author_browse | Becker, Ronald Fairbrother, Mark |
| author_facet | Becker, Ronald Fairbrother, Mark |
| author_sort | Fairbrother, Mark |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/10450 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:49.949Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/10450 Markov-Switching models and resultant equity implied volatility surfaces: a South African application Fairbrother, Mark Becker, Ronald Mathematics of Finance Includes bibliographical references. Standard Geometric Brownian Motion is the stock model underlying Black-Scholes famous option pricing formula. There are however numerous problems with this stock model as certain features do not follow some empirical stylised facts we see from the observation of actual asset prices. In particular, the constant parameter idea behind Geometric Brownian Motion is flawed. It is argued that information flow dictates stock price movements and information is a function macro-economic regimes shifts. As such, we propose an alternative model, one in which the parameters in the Standard Geometric Brownian Motion change according to an underlying Hidden Markov Process. This new model, termed a Markov-Switching model, is presented in extensive detail. Parameter Estimation methods, Simulation Methods and Option Pricing Theory are explored. Summary algorithms are presented so that this dissertation may be used as a good reference guide for those wishing to apply Markov-Switching Models. The model is tested by fitting the model on South African data and using the discussed option theory to create various implied volatility surfaces. The surfaces produced appear to obey some of the empirical observations and theoretical ideas around expected implied volatility surfaces, indicating that the Markov-Switching model has some value for option pricing. 2014-12-28T20:11:43Z 2014-12-28T20:11:43Z 2012 Master Thesis Masters MSc http://hdl.handle.net/11427/10450 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics of Finance Fairbrother, Mark Markov-Switching models and resultant equity implied volatility surfaces: a South African application |
| thesis_degree_str | Master's |
| title | Markov-Switching models and resultant equity implied volatility surfaces: a South African application |
| title_full | Markov-Switching models and resultant equity implied volatility surfaces: a South African application |
| title_fullStr | Markov-Switching models and resultant equity implied volatility surfaces: a South African application |
| title_full_unstemmed | Markov-Switching models and resultant equity implied volatility surfaces: a South African application |
| title_short | Markov-Switching models and resultant equity implied volatility surfaces: a South African application |
| title_sort | markov switching models and resultant equity implied volatility surfaces a south african application |
| topic | Mathematics of Finance |
| url | http://hdl.handle.net/11427/10450 |
| work_keys_str_mv | AT fairbrothermark markovswitchingmodelsandresultantequityimpliedvolatilitysurfacesasouthafricanapplication |