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Modelling illiquid volatility skews
Includes bibliographical references.
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| Format: | Thesis |
| Language: | English |
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Division of Actuarial Science
2014
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| _version_ | 1867613582430044160 |
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| access_status_str | Open Access |
| author | Crowther, Servaas Marcus |
| author2 | Mahomed, Obeid |
| author_browse | Crowther, Servaas Marcus Mahomed, Obeid |
| author_facet | Mahomed, Obeid Crowther, Servaas Marcus |
| author_sort | Crowther, Servaas Marcus |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/8529 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:38:26.535Z |
| 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 | 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:11427/8529 Modelling illiquid volatility skews Crowther, Servaas Marcus Mahomed, Obeid Taylor, David Mathematical Finance Includes bibliographical references. Most markets trade liquidly in options on the market index, in fact they often trade at a wide range of strike levels. Thus, using the Black-Scholes model, we can obtain the implied volatilities at the various strike levels, forming the associated implied volatility skew of the respective market under consideration. This, however, is not always feasible when it comes to the individual stocks within the market, as single stock options trade a lot less frequently. This dissertation makes use of data from the Eurozone, in particular we consider the Euro Stoxx 50 market index and its underlying constituents. Options written on the Euro Stoxx 50 and its constituents are highly liquid, and volatility skews are obtained for the market as well as for most of the single stocks within the market. I then artificially created 3 cases of illiquid markets, each with increasing degrees of sparseness mimicking various possible realities. Using principal component analysis, this dissertation aims to find an appropriate model for relating the volatility skew of the index to that of single stocks within the market in order to fill gaps in the data of the skews of the individual stocks. Results indicate that simpler models perform similarly in all scenarios of sparse- ness whereas the performance of more complex models decrease as the data becomes sparser. This indicates that basic relationships can be formed between the index and single stocks in cases with relatively low levels of trade in the market but more accurate estimates are more difficult to achieve. However, if we use the skew data, as is, as an input to the models, their performance remains by and far the same using the full data set and using monthly information. This is encouraging, as it means we can fill gaps in the individual stocks' skew data with as good a fit as if we modeled with a full set of data. 2014-10-17T10:09:57Z 2014-10-17T10:09:57Z 2014 Master Thesis Masters MPhil http://hdl.handle.net/11427/8529 eng Division of Actuarial Science Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Crowther, Servaas Marcus Modelling illiquid volatility skews |
| thesis_degree_str | Master's |
| title | Modelling illiquid volatility skews |
| title_full | Modelling illiquid volatility skews |
| title_fullStr | Modelling illiquid volatility skews |
| title_full_unstemmed | Modelling illiquid volatility skews |
| title_short | Modelling illiquid volatility skews |
| title_sort | modelling illiquid volatility skews |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/8529 |
| work_keys_str_mv | AT crowtherservaasmarcus modellingilliquidvolatilityskews |