Levy process with applications in finance and risk management

Abstract

This thesis aims to study numerical methods for approximating Lévy Semi-stationary process using Fourier methods. Initially, we introduce the fundamental theories for probability and numerical approximations, especially those of Lévy process. Based on these fundamental theories, we construct the numerical approximations using Fourier methods. We then investigate the error estimation produced by the above method with a proposition having rigorous mathematical formulation. Then, an application in path-option pricing is considered. Finally, a simulation for Variance Gamma Process, which derive from Lévy Process will be demonstrated. Key words: Financial Mathematics, Stochastic Processes, Lévy Process, Lévy Semi-stationary Process, Numerical Approximations, Fourier Methods, Derivatives Pricing.