In this thesis we price a Digital Double Barrier Basket option under the three-dimensional Black-Scholes model using the finite element method (FEM). We compute a benchmark solution for the FEM results with the Monte Carlo (MC) method. For each approach, we First explain the theory and then present our MATLAB implementation in detail. The implementation of the FEM is based on GeoPDEs, a suite of free software tools. We describe the structure of GeoPDEs as well as our o-scheme extension for handling time-dependent problems. Unlike the FEM, we implement the Monte Carlo method from scratch. After explaining the theory and the implementation, we examine the performance of each approach regarding its accuracy and computational costs. To complement the discussion on the approaches, we compare the FEM with the MC method focusing on the differences in the calculated option prices and the strains of the computer resources. We finish this thesis with a conclusion and a short outlook to further research. Supplemented by the free software suite GeoPDEs this thesis provides the full code to price a Digital Double Barrier Basket option with the finite element method and the Monte Carlo method.     «

In this thesis we price a Digital Double Barrier Basket option under the three-dimensional Black-Scholes model using the finite element method (FEM). We compute a benchmark solution for the FEM results with the Monte Carlo (MC) method. For each approach, we First explain the theory and then present our MATLAB implementation in detail. The implementation of the FEM is based on GeoPDEs, a suite of free software tools. We describe the structure of GeoPDEs as well as our o-scheme extension for...     »