On a Free Boundary Problem for an American Put Option Under the CEV Process
journal contributionposted on 2011-05-27, 00:00 authored by Miao Xu, Charles Knessl
We consider an American put option under the CEV process. This corresponds to a free boundary problem for a 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 use perturbation methods to find that the free boundary behaves differently for five ranges of time to expiry.
Publisher StatementNOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematics Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics Letters, [Vol 24, Issue 7, (July 2011)] DOI: 10.1016/j.aml.2011.02.006. The original publication is available at www.elsevier.com.