Swishchuk, AnatoliyMoyer, Zachary2015-02-032015-06-232015-02-032015http://hdl.handle.net/11023/2074We 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.engUniversity 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.Economics--FinanceMathematicsStatisticsGeometric Markov Renewal ProcessMarkovGeometric Brownian MotionMATLABBlack-ScholesEuropean OptionsAmerican OptionsMathematical FinanceAaseBinomialPoissonMarkov ChainMarkov processRegime-switchingStateDiscreteAsset modelMarket TrendsErgodicMergedDouble AveragedDiffusionNormal DeviationsNormal DeviatedRisk-neutralBlackScholesMertonCoxRossRubinsteinCallPutJumpJump modelPure jump modelOptimizationPerpetual AmericanStopping timeOptimal stopping timeGMRPGBMGeometric Compund Poisson ProcessGeometric Compund PoissonGCCPGCCLevy processLevyMarket incompletenessComplete marketApproximationBackwardationmaster thesis10.11575/PRISM/25963