Bounds on baskets option prices

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dc.contributor.advisorPolakow, Danielen_ZA
dc.contributor.authorDe Swardt, N Cen_ZA
dc.date.accessioned2014-07-31T08:07:02Z
dc.date.available2014-07-31T08:07:02Z
dc.date.issued2005en_ZA
dc.descriptionIncludes bibliographical references (leaves 70-71).
dc.description.abstractThe celebrated Black-Scholes option pricing model is unable to produce closed-form solutions for arithmetic basket options. This problem stems from the lack of an analitical form for the distribution of a sum of lognormal random variables. lVlarket participants commonly price basket options by assuming the basket follows lognormal dynamics, although it is known that this approximation performs poorly in some cicumstances. The problem of finding an analytical approximation to the sum of lognormally distributed random variables has been widely studied. In this dissertation we seek to draw these studies together and apply them in an option pricing setting. We propose some new option pricing formulae based on these approximations. In order to examine the utility of these new formulae and compare them to commonly used market approximations we present rigorous analytical bounds for the price of arithmetic basket options using the theory of comonotonicity. In this we follow the ideas in Deelstra et al. [7]. Additionally we provide an interval of hedge parameters (the Greeks). We carry out a numerical sensitivity analysis and identify circumstances under which the market approximation misprices basket options.en_ZA
dc.identifier.apacitationDe Swardt, N. C. (2005). <i>Bounds on baskets option prices</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/4880en_ZA
dc.identifier.chicagocitationDe Swardt, N C. <i>"Bounds on baskets option prices."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2005. http://hdl.handle.net/11427/4880en_ZA
dc.identifier.citationDe Swardt, N. 2005. Bounds on baskets option prices. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - De Swardt, N C AB - The celebrated Black-Scholes option pricing model is unable to produce closed-form solutions for arithmetic basket options. This problem stems from the lack of an analitical form for the distribution of a sum of lognormal random variables. lVlarket participants commonly price basket options by assuming the basket follows lognormal dynamics, although it is known that this approximation performs poorly in some cicumstances. The problem of finding an analytical approximation to the sum of lognormally distributed random variables has been widely studied. In this dissertation we seek to draw these studies together and apply them in an option pricing setting. We propose some new option pricing formulae based on these approximations. In order to examine the utility of these new formulae and compare them to commonly used market approximations we present rigorous analytical bounds for the price of arithmetic basket options using the theory of comonotonicity. In this we follow the ideas in Deelstra et al. [7]. Additionally we provide an interval of hedge parameters (the Greeks). We carry out a numerical sensitivity analysis and identify circumstances under which the market approximation misprices basket options. DA - 2005 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2005 T1 - Bounds on baskets option prices TI - Bounds on baskets option prices UR - http://hdl.handle.net/11427/4880 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/4880
dc.identifier.vancouvercitationDe Swardt NC. Bounds on baskets option prices. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2005 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/4880en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherFinancial Mathematicsen_ZA
dc.titleBounds on baskets option pricesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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