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Asymptotic Methods applied to an American Option under a CEV Process

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Title: Asymptotic Methods applied to an American Option under a CEV Process
Author(s): Xu, Miao
Advisor(s): Knessl, Charles
Contributor(s): Nicholls, David; Yang, Jie; Abramov, Rafael; Sclove, Stanley
Department / Program: Mathematics, Statistics, and Computer Science
Graduate Major: Applied Mathematics
Degree Granting Institution: University of Illinois at Chicago
Degree: PhD, Doctor of Philosophy
Genre: Doctoral
Subject(s): Asymptotic Methods Partial Differential Equations Mathematical Finance Analysis
Abstract: We 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.
Issue Date: 2012-12-07
Genre: thesis
URI: http://hdl.handle.net/10027/8921
Rights Information: Copyright 2011 Miao Xu
Date Available in INDIGO: 2012-12-07
2014-04-15
Date Deposited: 2011-08
 

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