Computational option pricing under jump diffusion and Lévy processes

The shortcomings of diffusion models in representing the risk related to large market movements have led to the development of various option pricing models with jumps. These models allow for a more realistic representation of price dynamics and greater flexibility in modelling and have therefore been the focus of much recent work. In this thesis the development of a robust finite difference method for the option pricing under jump-diffusion and Lévy processes is presented and its effectiveness is demonstrated on a range of pricing models