The Hunt Variance Gamma Process with Applications to Option Pricing

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dc.contributor.advisorMadan, Dilip Ben_US
dc.contributor.advisorBalan, Radu Ven_US
dc.contributor.authorAngelos, Bryanten_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2013-06-28T06:03:39Z
dc.date.available2013-06-28T06:03:39Z
dc.date.issued2013en_US
dc.description.abstractIn this dissertation we develop a spatially inhomogeneous Markov process as a model for financial asset prices. This model is called the Hunt variance gamma process. We define it via its infinitesimal generator and prove that this generator induces a unique measure on the space of cadlag functions. We next describe a procedure to do computations with this model by finding a continuous-time Markov chain approximation. This approximation is used to calibrate the model to fit the S&P 500 futures option surface. Next we investigate specific characteristics of the process, showing how it differs from both Levy and Sato processes. We conclude by using the calibrated model to answer questions about properties of the risk-neutral distribution of future stock prices. We observe a more accurate fit to the risk-neutral term structure of volatility, skewness, and kurtosis, and the presence of mean-reversion in conditional probabilities involving large jumps.en_US
dc.identifier.urihttp://hdl.handle.net/1903/14029
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledApplied mathematicsen_US
dc.subject.pquncontrolledFinancial Derivativeen_US
dc.subject.pquncontrolledHunt Processen_US
dc.subject.pquncontrolledLevy Processen_US
dc.subject.pquncontrolledMathematical Finanaceen_US
dc.subject.pquncontrolledOptionen_US
dc.titleThe Hunt Variance Gamma Process with Applications to Option Pricingen_US
dc.typeDissertationen_US

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