Methods for calculating option prices with early-exercise features

Abstract

In this dissertation we deal with two distinct methods for pricing financial options with early-exercise features. First we use finite difference methods to calculate the prices, examining in particular two new schemes designed to deal with problems where the problems becomes singly perturbed. The second method is MonteCarlo techniques which allow for the early exercise of the option using different techniques to determine whether or not it is optimal to exercise early. Two new algorithms in particular were developed, one which uses an interpolation method to calculate the expected payoffs, the other uses an iterative technique and Ito's Lemma to determine if the option should be exercised.