This thesis is divided into 4 chapters. Chapter 1 gives a brief explanation of what the Greeks are and why they are of interest in applied financial mathematics. There is also a short summary of the first attempts at numerical methods to calculate the Greeks as well as an introduction to Lévy processes.
Chapter 2 starts with some relevant results from Malliavin Calculus and proceeds to derivations of general expressions for the most important Greeks using Malliavin weights. It concludes with a mathematical argument that shows how these weights can be regarded as optimal.
Chapter 3 introduces stochastic volatility models followed by some more detailed analysis of a specific stochastic volatility model called the Barndorff-Nielsen and Shephard model. The technicalities involved in doing the necessary simulations for this model are discussed and implemented in Matlab.
Chapter 4 contains a summary and outlines possible extensions to this thesis.