Mean-variance hedging in an illiquid market

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dc.contributor.advisorEbobisse Bille, Francoisen_ZA
dc.contributor.authorMavuso, Melusi Manqobaen_ZA
dc.date.accessioned2015-12-04T18:06:52Z
dc.date.available2015-12-04T18:06:52Z
dc.date.issued2015en_ZA
dc.description.abstractConsider a market consisting of two correlated assets: one liquidly traded asset and one illiquid asset that can only be traded at time 0. For a European derivative written on the illiquid asset, we find a hedging strategy consisting of a constant (time 0) holding in the illiquid asset and dynamic trading strategies in the liquid asset and a riskless bank account that minimizes the expected square replication error at maturity. This mean-variance optimal strategy is first found when the liquidly traded asset is a local martingale under the real world probability measure through an application of the Kunita-Watanabe projection onto the space of attainable claims. The result is then extended to the case where the liquidly traded asset is a continuous square integrable semimartingale, and we again use the Kunita-Watanabe decomposition, now under the variance optimal martingale measure, to find the mean-variance optimal strategy in feedback form. In an example, we consider the case where the two assets are driven by correlated Brownian motions and the derivative is a call option on the illiquid asset. We use this example to compare the terminal hedging profit and loss of the optimal strategy to a corresponding strategy that does not use the static hedge in the illiquid asset and conclude that the use of the static hedge reduces the expected square replication error significantly (by up to 90% in some cases). We also give closed form expressions for the expected square replication error in terms of integrals of well-known special functions.en_ZA
dc.identifier.apacitationMavuso, M. M. (2015). <i>Mean-variance hedging in an illiquid market</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/15595en_ZA
dc.identifier.chicagocitationMavuso, Melusi Manqoba. <i>"Mean-variance hedging in an illiquid market."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2015. http://hdl.handle.net/11427/15595en_ZA
dc.identifier.citationMavuso, M. 2015. Mean-variance hedging in an illiquid market. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Mavuso, Melusi Manqoba AB - Consider a market consisting of two correlated assets: one liquidly traded asset and one illiquid asset that can only be traded at time 0. For a European derivative written on the illiquid asset, we find a hedging strategy consisting of a constant (time 0) holding in the illiquid asset and dynamic trading strategies in the liquid asset and a riskless bank account that minimizes the expected square replication error at maturity. This mean-variance optimal strategy is first found when the liquidly traded asset is a local martingale under the real world probability measure through an application of the Kunita-Watanabe projection onto the space of attainable claims. The result is then extended to the case where the liquidly traded asset is a continuous square integrable semimartingale, and we again use the Kunita-Watanabe decomposition, now under the variance optimal martingale measure, to find the mean-variance optimal strategy in feedback form. In an example, we consider the case where the two assets are driven by correlated Brownian motions and the derivative is a call option on the illiquid asset. We use this example to compare the terminal hedging profit and loss of the optimal strategy to a corresponding strategy that does not use the static hedge in the illiquid asset and conclude that the use of the static hedge reduces the expected square replication error significantly (by up to 90% in some cases). We also give closed form expressions for the expected square replication error in terms of integrals of well-known special functions. DA - 2015 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2015 T1 - Mean-variance hedging in an illiquid market TI - Mean-variance hedging in an illiquid market UR - http://hdl.handle.net/11427/15595 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/15595
dc.identifier.vancouvercitationMavuso MM. Mean-variance hedging in an illiquid market. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2015 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/15595en_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.titleMean-variance hedging in an illiquid marketen_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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