Pricing of European, Bermudan and American Options under the
Exponential Variance Gamma Process

Abstract

This dissertation reports on a study of the pricing of European, Bermudan and American put options where the stock price is driven by an exponential Variance Gamma process. Closed-form solutions (for European options), Monte Carlo methods (for Bermudan options) and Finite Difference methods (for all three types) were implemented to value the options. The performance of the various algorithms was investigated and the option values produced by the different algorithms were compared. Finally, the delta and gamma greeks were calculated for these options using finite difference and Monte Carlo methods.