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Asymptotic Methods applied to an American Option under a CEV Process
thesis
posted on 2012-12-07, 00:00 authored by Miao XuWe 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.
History
Advisor
Knessl, CharlesDepartment
Mathematics, Statistics, and Computer ScienceDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral
Committee Member
Nicholls, David Yang, Jie Abramov, Rafael Sclove, StanleySubmitted date
2011-08Language
- en
Issue date
2012-12-07Usage metrics
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