On multigrid for linear complementarity problems with application to American-style options.

Abstract

We discuss a nonlinear multigrid method for 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 convectiondiffusion 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.