Pricing American Options by the Finite Element Method

In this paper we investigate the performances of high-order of finite element methods for American option pricing. First of all, the partial differential problem that yields the price of American options, which is a free boundary problem, is transformed to a problem with a fixed boundary by adding a suitable penalty term. Then, by employing a quadratic finite element method, a nonlinear system of differential equations is obtained which is solved using an ad-hoc implicit-explicit Euler time-stepping. Numerical results will be presented to demonstrate the validity and the effectiveness of the method proposed.