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dc.contributor.advisorKnessl, Charlesen_US
dc.contributor.authorXu, Miaoen_US
dc.date.accessioned2012-12-07T11:56:02Z
dc.date.available2012-12-07T11:56:02Z
dc.date.available2014-04-15T09:30:39Z
dc.date.created2011-08en_US
dc.date.issued2012-12-07
dc.date.submitted2011-08en_US
dc.identifier.urihttp://hdl.handle.net/10027/8921
dc.description.abstractWe consider an American put option under the Constant Elasticity of Variance (CEV) process. This corresponds to a free boundary problem for a partial differential equation (PDE). We show that this free boundary satisfies a nonlinear integral equation, and analyze it in the limit of small $\rho$ = $2r/ \sigma^2$, where $r$ is the interest rate and $\sigma$ is the volatility. We find that the free boundary behaves differently for five ranges of time to expiry. We then analyze option price $P(S,t)$, as a function of the asset price $S$ and time to expiry $t$. We obtain the asymptotic expansion of $P$ as $\rho \rightarrow 0$, first via an integral equation formulation, and then using the PDE satisfied by $P$, and analyzing it by perturbation theory and matched asymptotic expansions.en_US
dc.language.isoenen_US
dc.rightsCopyright 2011 Miao Xu
dc.subjectAsymptotic Methodsen_US
dc.subjectPartial Differential Equationsen_US
dc.subjectMathematical Financeen_US
dc.subjectAnalysisen_US
dc.titleAsymptotic Methods applied to an American Option under a CEV Processen_US
thesis.degree.departmentMathematics, Statistics, and Computer Scienceen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Illinois at Chicagoen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePhD, Doctor of Philosophyen_US
dc.type.genrethesisen_US
dc.contributor.committeeMemberNicholls, Daviden_US
dc.contributor.committeeMemberYang, Jieen_US
dc.contributor.committeeMemberAbramov, Rafaelen_US
dc.contributor.committeeMemberSclove, Stanleyen_US
dc.type.materialtexten_US


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