Pricing barrier and barrier crack option under levy process

In this thesis we study and analyze the pricing of barrier and barrier crack options under a Time-Changed Levy process. Oil and gasoline in Canada are our underlying commodities of interest in this study. To characterize the dynamics of oil and gasoline prices, Black-Scholes and Time-Changed models based on Levy process are proposed. To verify the model, real data of the Canada oil and gas market is used. While the pricing methods based on Monte Carlo are the well-known and dominant for price calculation, we propose a Fourier Transform (FT) for the pricing, which provide some important advantages to the Monte Carlo method such as computation speed without compromising any accuracy. The method is also applied to Crack spread contracts to reduce the risk.