Pricing Volatility Derivatives Using Space Scaled Levy Processes

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dc.contributor.advisorMadan, Dilip Ben_US
dc.contributor.advisorvon Petersdorff, Tobiasen_US
dc.contributor.authorPrakash, Samviten_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2009-01-24T06:34:11Z
dc.date.available2009-01-24T06:34:11Z
dc.date.issued2008-09-02en_US
dc.description.abstractThe VIX index measures the one-month risk-neutral forward volatility of the S&P500 (SPX) index. While Lévy processes such as the CGMY process can price options on the underlying stock or index, they implicitly assume a constant forward volatility. This makes them unsuitable for pricing options on VIX. We propose a model within the one dimensional Markovian framework for pricing VIX and SPX options simultaneously. We introduce space dependence of volatility by scaling the CGMY process with a leverage function. The resultant process can consistently price options on SPX and VIX of a given maturity. We also perform surface calibrations of options on the two indices separately. We explore the properties of the implied distribution of the SPX from both indices and conclude that the VIX index under-weighs small jumps as compared to large jumps as well as the skewness of the SPX index .en_US
dc.format.extent471098 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/8742
dc.language.isoen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledEconomics, Financeen_US
dc.subject.pqcontrolledComputer Scienceen_US
dc.subject.pquncontrolledVIX Options Pricingen_US
dc.subject.pquncontrolledVolatility Derivatives Pricingen_US
dc.subject.pquncontrolledSpace Scaled Levy Processesen_US
dc.subject.pquncontrolledJoint Calibration of S&P500 and VIX Optionsen_US
dc.titlePricing Volatility Derivatives Using Space Scaled Levy Processesen_US
dc.typeDissertationen_US

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