Modelling illiquid volatility skews

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dc.contributor.advisorMahomed, Obeiden_ZA
dc.contributor.advisorTaylor, Daviden_ZA
dc.contributor.authorCrowther, Servaas Marcusen_ZA
dc.date.accessioned2014-10-17T10:09:57Z
dc.date.available2014-10-17T10:09:57Z
dc.date.issued2014en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractMost 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.en_ZA
dc.identifier.apacitationCrowther, S. M. (2014). <i>Modelling illiquid volatility skews</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/8529en_ZA
dc.identifier.chicagocitationCrowther, Servaas Marcus. <i>"Modelling illiquid volatility skews."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2014. http://hdl.handle.net/11427/8529en_ZA
dc.identifier.citationCrowther, S. 2014. Modelling illiquid volatility skews. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Crowther, Servaas Marcus AB - 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. DA - 2014 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2014 T1 - Modelling illiquid volatility skews TI - Modelling illiquid volatility skews UR - http://hdl.handle.net/11427/8529 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/8529
dc.identifier.vancouvercitationCrowther SM. Modelling illiquid volatility skews. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2014 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/8529en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDivision of Actuarial Scienceen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Financeen_ZA
dc.titleModelling illiquid volatility skewsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhilen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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