Adaptive finite differences to price European options under the Bates model

Abstract: This thesis presents the pricing of European options under the Bates model, using adaptivity in order to efficiently distribute the grid points in space. For a fixed number of grid points the size of the absolute error, when using the adaptive approach, is reduced compared to the corresponding equidistant grid. Since the adaptive method needs less grid points for a certain error, the linear system of equations that needs to be solved becomes smaller and the memory costs are reduced. The implementation does not rest upon heavy optimization or parallelization theory, but nevertheless it solves the problem flawlessly and the adaptive method outperforms the equidistant method regarding computational time when keeping the error at a predefined level.