Stable processes: theory and applications in finance

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dc.contributor.advisorMataramvura, Sureen_ZA
dc.contributor.advisorTaylor, Daviden_ZA
dc.contributor.authorKateregga, Michaelen_ZA
dc.date.accessioned2018-01-29T07:27:22Z
dc.date.available2018-01-29T07:27:22Z
dc.date.issued2017en_ZA
dc.description.abstractThis thesis is a study on stable distributions and some of their applications in understanding financial markets. Three broad problems are explored: First, we study a parameter and density estimation problem for stable distributions using commodity market data. We investigate and compare the accuracy of the quantile, logarithmic, maximum likelihood (ML) and empirical characteristic function (ECF) methods. It turns out that the ECF is the most recommendable method, challenging literature that instead suggests the ML. Secondly, we develop an affine theory for subordinated random processes and apply the results to pricing commodity futures in markets where the spot price includes jumps. The jumps are introduced by subordinating Brownian motion in the spot model by an α-stable process, α ε (0; 1] which leads to a new pricing approach for models with latent variables. The third problem is the pricing of general derivatives and risk management based on Malliavin calculus. We derive a Bismut-Elworthy-Li (BEL) representation formula for computing financial Greeks under the framework of subordinated Brownian motion by an inverse α-stable process with α ε (0; 1]. This subordination by an inverse α-stable process allows zero returns in the model rendering it fit for illiquid emerging markets. In addition, we demonstrate that the model is best suited for pricing derivatives with irregular payoff functions compared to the traditional Euler methods.en_ZA
dc.identifier.apacitationKateregga, M. (2017). <i>Stable processes: theory and applications in finance</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/27069en_ZA
dc.identifier.chicagocitationKateregga, Michael. <i>"Stable processes: theory and applications in finance."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2017. http://hdl.handle.net/11427/27069en_ZA
dc.identifier.citationKateregga, M. 2017. Stable processes: theory and applications in finance. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Kateregga, Michael AB - This thesis is a study on stable distributions and some of their applications in understanding financial markets. Three broad problems are explored: First, we study a parameter and density estimation problem for stable distributions using commodity market data. We investigate and compare the accuracy of the quantile, logarithmic, maximum likelihood (ML) and empirical characteristic function (ECF) methods. It turns out that the ECF is the most recommendable method, challenging literature that instead suggests the ML. Secondly, we develop an affine theory for subordinated random processes and apply the results to pricing commodity futures in markets where the spot price includes jumps. The jumps are introduced by subordinating Brownian motion in the spot model by an α-stable process, α ε (0; 1] which leads to a new pricing approach for models with latent variables. The third problem is the pricing of general derivatives and risk management based on Malliavin calculus. We derive a Bismut-Elworthy-Li (BEL) representation formula for computing financial Greeks under the framework of subordinated Brownian motion by an inverse α-stable process with α ε (0; 1]. This subordination by an inverse α-stable process allows zero returns in the model rendering it fit for illiquid emerging markets. In addition, we demonstrate that the model is best suited for pricing derivatives with irregular payoff functions compared to the traditional Euler methods. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Stable processes: theory and applications in finance TI - Stable processes: theory and applications in finance UR - http://hdl.handle.net/11427/27069 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/27069
dc.identifier.vancouvercitationKateregga M. Stable processes: theory and applications in finance. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/27069en_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.otherActuarial Scienceen_ZA
dc.titleStable processes: theory and applications in financeen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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