On a Free Boundary Problem for an American Put Option Under the CEV Process
journal contributionposted on 27.05.2011, 00:00 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.