Modeling of Currency Trading Markets and Pricing Their Derivatives in a Markov Modulated Environment

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atmire.migration.oldid2157
dc.contributor.advisorSwishchuk, Anatoliy
dc.contributor.advisorElliott, Robert
dc.contributor.authorTertychnyi, Maksym
dc.date.accessioned2014-05-08T18:12:59Z
dc.date.available2014-06-16T07:00:44Z
dc.date.issued2014-05-08
dc.date.submitted2014en
dc.description.abstractUsing a Levy process we generalize formulas in Bo et al. (2010) to the Esscher transform parameters for the log-normal distribution which ensures the martingale condition holds for the discounted foreign exchange rate. We also derive similar results, but in the case when the dynamics of the FX rate is driven by a general Merton jump-diffusion process. Using these values of the parameters we find a risk-neural measure and provide new formulas for the distribution of jumps, the mean jump size, and the Poisson process intensity with respect to this measure. The formulas for a European call foreign exchange option are also derived. We apply these formulas to the case of the log-double exponential and exponential distribution of jumps. We provide numerical simulations for the European call foreign exchange option prices with different parameters.en_US
dc.identifier.citationTertychnyi, M. (2014). Modeling of Currency Trading Markets and Pricing Their Derivatives in a Markov Modulated Environment (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26947en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/26947
dc.identifier.urihttp://hdl.handle.net/11023/1514
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.subjectEducation--Mathematics
dc.subject.classificationForeign exchange rateen_US
dc.subject.classificationEsscher transformen_US
dc.subject.classificationRisk-neutral measureen_US
dc.subject.classificationEuropean call optionen_US
dc.subject.classificationLevy processesen_US
dc.subject.classificationMarkov processesen_US
dc.titleModeling of Currency Trading Markets and Pricing Their Derivatives in a Markov Modulated Environment
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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