A new approach for numerical identification of optimal exercise curve

Abstract

This paper deals with American put options, which is modelled by a free boundary problem for a nonhomogeneous generalized Black-Scholes equation. We present a parameter estimation technique to compute the put option price as well as the optimal exercise curve. The forward problem of computing the put option price with a given parameter of the function space for the free boundary employs the upwind finite difference scheme. The inverse problem of minimizing the cost functional over that function space uses the Levenberg-Marquardt method. Numerical experiments show that the approximation scheme satisfies appropriate convergence properties. Our method can be applied to the case that the volatility is a function of time and asset variables.