Parameter Estimation of the Heston Volatility Sde under the Non-Gaussian Regime

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dc.contributor.advisorAzencott, Robert
dc.contributor.committeeMemberTimofeyev, Ilya
dc.contributor.committeeMemberTörök, Andrew
dc.contributor.committeeMemberGunaratne, Gemunu H.
dc.creatorSaha, Dipanwita 1990-
dc.date.accessioned2019-05-23T14:44:01Z
dc.date.createdAugust 2018
dc.date.issued2018-08
dc.date.submittedAugust 2018
dc.date.updated2019-05-23T14:44:02Z
dc.description.abstractStochastic volatility models, in finance, study the volatility dynamics of the asset pricing process. It is the assumption of the randomness of the volatility of a underlying asset not directly observable, that allows for these models to improve the accuracy of computation of the pricing process and its forecasts. Stochastic Differential equations (SDEs) model such randomness in volatility along with the pricing process. Heston model is a widely used stochastic volatility model that goverened by five unknown parameters. Estimation of these parameters help us obtain an evolution for assest price and its corresponding volatility process that is consistent with real time option prices. In this thesis, we investigate the behaviour of the Maximum likelihood estimates for the parameters of the Heston model in a non-Gaussian regime. In particular, we study the MLEs when the ratio of the parameters of the volatility equation of the Heston model, satisfying the classical Feller condition, falls under a certain critical value. We demonstrate that the asymptotic behavior of parameters can be described as rational functions which involve variables following the stable distribution. We also develop a strategy to estimate parameters of the stable distribution and verify our approach using numerical simulations.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10657/4003
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.subjectStochastic volatility
dc.subjectStochastic differential equations (SDE)
dc.subjectHeston model
dc.subjectParameter estimation
dc.subjectMLE
dc.subjectStable distribution
dc.titleParameter Estimation of the Heston Volatility Sde under the Non-Gaussian Regime
dc.type.dcmiText
dc.type.genreThesis
local.embargo.lift2020-08-01
local.embargo.terms2020-08-01
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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