Option pricing problems are characterized by multidimensional second-order parabolic partial differential equations that in general do not possess an analytical solution. Conventional PDE solvers on full grids need O(2^nd) grid points to provide a solution of accuracy O(2^-np), where d is the dimensionality of the problem, 2^-n the mesh size and p the accuracy of the underlying discretization scheme. In contrast, in the context of elliptical PDEs the sparse grid combination technique has been proved to generate a O(^n(d-1)*2^-np) accurate solution involving only O(n^(d-1)*2^n) degrees of freedom. In this thesis we analyze the use of the sparse grid combination technique for the solution of di¤erent option contracts: a European call option, an Asian option as well as a cliquet contract and a guarantee on spending funded by endowments. We show that, in general, the combination approach exhibits the expected approximation properties, especially for a fully implicit discretization of the PDE. For practical purposes the obtained results are usually sufficient.     «

Option pricing problems are characterized by multidimensional second-order parabolic partial differential equations that in general do not possess an analytical solution. Conventional PDE solvers on full grids need O(2^nd) grid points to provide a solution of accuracy O(2^-np), where d is the dimensionality of the problem, 2^-n the mesh size and p the accuracy of the underlying discretization scheme. In contrast, in the context of elliptical PDEs the sparse grid combination technique has been pr...     »