Pricing American Options by the Finite Element Method

In this paper we investigate the performances of high-order of nite element methods forAmerican option pricing. First of all, the partial di erential problem that yields the priceof American options, which is a free boundary problem, is transformed to a problem witha xed boundary by adding a suitable penalty term. Then, by employing a quadratic niteelement method, a nonlinear system of di erential equations is obtained which is solvedusing an ad-hoc implicit-explicit Euler time-stepping. Numerical results will be presented todemonstrate the validity and the e ectiveness of the method proposed.

Pricing American Options by the Finite Element Method Keywords:

American Option , Penalty Method , Finite Element Method , Explicit and Implicit Algorithm , Newton Mtheod