European and American Option Pricing with a Geometric Markov Renewal Process Underlying Asset Model

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atmire.migration.oldid2969
dc.contributor.advisorSwishchuk, Anatoliy
dc.contributor.authorMoyer, Zachary
dc.date.accessioned2015-02-03T17:51:47Z
dc.date.available2015-06-23T07:00:39Z
dc.date.issued2015-02-03
dc.date.submitted2015en
dc.description.abstractWe present methods for pricing of American and European options under a Geometric Markov Renewal Process (GMRP) as the underlying asset model. We provide a detailed overview of the GMRP. Discussions of Markov processes, Geometric Brownian Motion, and GMRP approximation techniques are presented. We discuss the Aase trading model, with a MATLAB implementation. We discuss the Black-Scholes and binomial Cox-Ross-Rubinstein formulas for European and American options. We present results on Fixed Time Increments GMRP, with a derivation of a method for a limiting case of Fixed Time Increments GMRP (applicable to perpetual American options), complete with MATLAB implementations. We also present a MATLAB implementation for the pricing of European options under GMRP with an arbitrary jump distribution. We discuss diffusion and normal deviated approximations of a GMRP, and present MATLAB implementations for pricing American and European options. We follow this with a discussion of a Poisson approximation of a security market. A literature review is presented, together with an appendix including our MATLAB implementations. Conclusions and recommendations for future research directions conclude the paper.en_US
dc.identifier.citationMoyer, Z. (2015). European and American Option Pricing with a Geometric Markov Renewal Process Underlying Asset Model (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25963en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/25963
dc.identifier.urihttp://hdl.handle.net/11023/2074
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectEconomics--Finance
dc.subjectMathematics
dc.subjectStatistics
dc.subject.classificationGeometric Markov Renewal Processen_US
dc.subject.classificationMarkoven_US
dc.subject.classificationGeometric Brownian Motionen_US
dc.subject.classificationMATLABen_US
dc.subject.classificationBlack-Scholesen_US
dc.subject.classificationEuropean Optionsen_US
dc.subject.classificationAmerican Optionsen_US
dc.subject.classificationMathematical Financeen_US
dc.subject.classificationAaseen_US
dc.subject.classificationBinomialen_US
dc.subject.classificationPoissonen_US
dc.subject.classificationMarkov Chainen_US
dc.subject.classificationMarkov processen_US
dc.subject.classificationRegime-switchingen_US
dc.subject.classificationStateen_US
dc.subject.classificationDiscreteen_US
dc.subject.classificationAsset modelen_US
dc.subject.classificationMarket Trendsen_US
dc.subject.classificationErgodicen_US
dc.subject.classificationMergeden_US
dc.subject.classificationDouble Averageden_US
dc.subject.classificationDiffusionen_US
dc.subject.classificationNormal Deviationsen_US
dc.subject.classificationNormal Deviateden_US
dc.subject.classificationRisk-neutralen_US
dc.subject.classificationBlacken_US
dc.subject.classificationScholesen_US
dc.subject.classificationMertonen_US
dc.subject.classificationCoxen_US
dc.subject.classificationRossen_US
dc.subject.classificationRubinsteinen_US
dc.subject.classificationCallen_US
dc.subject.classificationPuten_US
dc.subject.classificationJumpen_US
dc.subject.classificationJump modelen_US
dc.subject.classificationPure jump modelen_US
dc.subject.classificationOptimizationen_US
dc.subject.classificationPerpetual Americanen_US
dc.subject.classificationStopping timeen_US
dc.subject.classificationOptimal stopping timeen_US
dc.subject.classificationGMRPen_US
dc.subject.classificationGBMen_US
dc.subject.classificationGeometric Compund Poisson Processen_US
dc.subject.classificationGeometric Compund Poissonen_US
dc.subject.classificationGCCPen_US
dc.subject.classificationGCCen_US
dc.subject.classificationLevy processen_US
dc.subject.classificationLevyen_US
dc.subject.classificationMarket incompletenessen_US
dc.subject.classificationComplete marketen_US
dc.subject.classificationApproximationen_US
dc.subject.classificationBackwardationen_US
dc.titleEuropean and American Option Pricing with a Geometric Markov Renewal Process Underlying Asset Model
dc.typemaster thesis
thesis.degree.disciplineMathematics and Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.item.requestcopytrue
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