Pricing Multi-Asset Options with Multivariate Variance Gamma and Normal Inverse Gaussian Processes Using the Fourier Space Time-Stepping Method

dc.contributor.advisorKao, Edward P. C.
dc.contributor.committeeMemberAuchmuty, Giles
dc.contributor.committeeMemberBodmann, Bernhard G.
dc.contributor.committeeMemberHeier, Gordon
dc.contributor.committeeMemberPirrong, Craig
dc.creatorMeerscheidt, Kyle 1982-
dc.creator.orcid0000-0002-9256-2291
dc.date.accessioned2019-09-10T16:14:03Z
dc.date.createdDecember 2018
dc.date.issued2018-12
dc.date.submittedDecember 2018
dc.date.updated2019-09-10T16:14:04Z
dc.description.abstractWe use a multivariate variance gamma process developed by Jun Wang (2009) and a similarly constructed multivariate normal inverse Gaussian process to price multi-asset options and calculate greeks with the Fourier space time-stepping (FST) method introduced by Jackson, Jaimungal, and Surkov (2007). The prices are checked against Monte Carlo simulations to demonstrate their accuracy, and we see a marked improvement in computational efficiency. Included are options on the spark spread, the crack spread, and the crush spread, as well as other exotic options that are difficult to price with existing methods. We also adopt a parameter estimation method by Cervellera and Tucci (2016) for variance gamma processes, and adapt it for use with normal inverse Gaussian processes, to make parameter estimates for the marginal processes that are robust with respect to small perturbations of the data.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10657/4437
dc.language.isoeng
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectLévy processes
dc.subjectVariance gamma
dc.subjectNormal inverse gaussian
dc.subjectMulti-asset
dc.subjectOptions
dc.subjectPricing
dc.subjectHedging
dc.subjectMonte Carlo
dc.subjectGreeks
dc.subjectMultivariate
dc.subjectFourier space time-stepping
dc.titlePricing Multi-Asset Options with Multivariate Variance Gamma and Normal Inverse Gaussian Processes Using the Fourier Space Time-Stepping Method
dc.type.dcmiText
dc.type.genreThesis
local.embargo.lift2020-12-01
local.embargo.terms2020-12-01
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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