Stochastic time-changed Lévy processes with their implementation

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dc.contributor.advisorMataramvura, Sureen_ZA
dc.contributor.authorSihlobo, Odwaen_ZA
dc.date.accessioned2015-06-29T07:46:30Z
dc.date.available2015-06-29T07:46:30Z
dc.date.issued2014en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractWe focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters.en_ZA
dc.identifier.apacitationSihlobo, O. (2014). <i>Stochastic time-changed Lévy processes with their implementation</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/13156en_ZA
dc.identifier.chicagocitationSihlobo, Odwa. <i>"Stochastic time-changed Lévy processes with their implementation."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2014. http://hdl.handle.net/11427/13156en_ZA
dc.identifier.citationSihlobo, O. 2014. Stochastic time-changed Lévy processes with their implementation. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Sihlobo, Odwa AB - We focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters. DA - 2014 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2014 T1 - Stochastic time-changed Lévy processes with their implementation TI - Stochastic time-changed Lévy processes with their implementation UR - http://hdl.handle.net/11427/13156 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/13156
dc.identifier.vancouvercitationSihlobo O. Stochastic time-changed Lévy processes with their implementation. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2014 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/13156en_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.otherFinancial Mathematicsen_ZA
dc.titleStochastic time-changed Lévy processes with their implementationen_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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