Iterative methods for option pricing in Merton's Jump diffusion model

The main purpose of this thesis is to study numerical schemes for the solution of the PDE associated with the Merton jump-diffusion model. The implementation of these schemes will be achieved through the finite differences method, and in particular two implicit methods (Backward Euler and Crank-Nicolson) will be developed. The linear systems created will be solved by two iterative methods, namely Multigrid and GMRES; for the latter, the effectiveness of using some preconditioners will be tested. Moreover, an explicit-implicit scheme will be applied with the Backward Euler method and it will be resolved by the direct method Tridiagonal solver.