Modelling illiquid volatility skews

 

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dc.contributor.advisor Mahomed, Obeid en_ZA
dc.contributor.advisor Taylor, David en_ZA
dc.contributor.author Crowther, Servaas Marcus en_ZA
dc.date.accessioned 2014-10-17T10:09:57Z
dc.date.available 2014-10-17T10:09:57Z
dc.date.issued 2014 en_ZA
dc.identifier.citation Crowther, S. 2014. Modelling illiquid volatility skews. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/8529
dc.description Includes bibliographical references. en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematical Finance en_ZA
dc.title Modelling illiquid volatility skews en_ZA
dc.type Thesis / Dissertation en_ZA
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Commerce en_ZA
dc.publisher.department Division of Actuarial Science en_ZA
dc.type.qualificationlevel Masters en_ZA
dc.type.qualificationname MPhil en_ZA
uct.type.filetype Text
uct.type.filetype Image


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