Option Pricing and Early Exercise Boundary of American Options under Markov-Modulated Volatility

Sammanfattning: The CRR binomial model is one of the most important models in financial mathematics. In this thesis we consider an extension to this model with Markov switching-state volatility. We present a detailed algorithm for obtaining early exercise boundaries for American options, as well as, fair prices for both American and European options. To provide extensive numerical results, we experiment with different variations of the parameters and analyze the results. In particular, we study properties of the resulting early exercise boundaries. Moreover, we give three approximation methods for the pricing of European options under this model.