On Multigrid for Linear Complementarity Problems with Application to American-style Options

C. W. Oosterlee
GMD, Institute for Algorithms and Scientific Computing
D-53754 Sankt Augustin, Germany


Abstract

We discuss a nonlinear multigrid methodfor a linear complementarity problem. The convergence is improved by a recombination of iterants. The problem under consideration deals with option pricing from mathematical finance. Linear complementarity problems arise from so-called American-style options. A 2D convection-diffusion type operator is discretized with the help of second order upwind discretizations. The properties of smoothers are analyzed with Fourier two-grid analysis. Numerical solutions obtained for the option pricing problem are compared with reference results.

Key words. linear complementarity problems, American-style options, nonlinear multigrid, projected Gauss-Seidel, iterant recombination, second-order upwind discretization, Fourier analysis

AMS subject classifications. 65M55, 65F99, 90A09