Volume 15, pp. 165-185, 2003.

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

C. W. Oosterlee

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 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.

Full Text (PDF) [465 KB], BibTeX

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

Links to the cited ETNA articles

[20]	Vol. 6 (1997), pp. 271-290 T. Washio and C. W. Oosterlee: Krylov subspace acceleration for nonlinear multigrid schemes

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