**Date & Time:** Thursday, January 29, 2009, 11:30-12:30.

**Venue:** Ramanujan Hall

**Title:** Finite Element Methods for American Options; A Penalty Approach

**Speaker:** Sajid Memon, IIT Bombay

**Abstract:** In finance, the price of an American option is obtained from the price of the underlying asset by solving a linear complementarity problem. In this article, penalty function approach to the pricing of American option is presented. The problem is first reformulated as a variational inequality problem; the resulting variational inequality problem is then transformed into a non-linear parabolic partial differential equation. Existence, uniqueness, and regularity results are derived using a priori bounds. The error associated with the penalty approximation to the variational inequality problem is analyzed. Finite element method is applied to the penalized problem and by coupling the penalty parameter *ε* and the discretization parameters *h* and *Δt*, error estimates in appropriate norm are established. Numerical results are given to illustrate the theoretical findings and to show the effectiveness and usefulness of the method.