Pricing of American options

Abstract

Pricing of American options using Black-Scholes equation is difficult since it is a moving boundary problem. Black-Scholes only calculates the option price at one point in time, i.e. at expiration. It does not consider the steps along the way where there could be the possibility of early exercise of an American option. Solving such problems using numerical techniques is highly time consuming and leads to accuracy issues. Therefore, we need to study the algorithms that have been tried thus far and attempt to improve those models and apply them to other complex financial products.