On a free boundary problem for an American put option under the CEV process

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 ρ=2r/σ2ρ=2r/σ2, where rr is the interest rate and σσ is the volatility. We use perturbation methods to find that the free boundary behaves differently for five ranges of time to expiry.