Finite Element Method for American Option Pricing: a Penalty Approach

The model for pricing of American option gives rise to a parabolic variational inequality. We first use penalty function approach to reformulate it as an equality problem. Since the problem is defined on an unbounded domain, we truncate it to a bounded domain and discuss error due to truncation and penalization. Finite element method is then applied to the penalized problem on the truncated domain. By coupling the penalty parameter and the discretization parameters, error estimates are established when the initial data in H 0 . Finally, some numerical experiments are conducted to confirm the theoretical findings.