The multigrid algorithm applied to a degenerate equation: A convergence analysis

Authors:
Ariel Almendral Vázquez;Bjørn Fredrik Nielsen
Affiliations:
Norwegian Computing Center, Gaustadalleen 23, Postbox 114, Blindern, N-0314, Oslo, Norway;Simula Research Laboratory, P.O.Box 134, 1325 Lysaker, Norway
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 2
Cited 0

Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Uniform convergence of the multigrid V-cycle for an anisotropic problem

Mathematics of Computation

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Abstract

In this paper we analyze the convergence properties of the Multigrid Method applied to the Black-Scholes differential equation arising in mathematical finance. We prove, for the discretized single-asset Black-Scholes equation, that the multigrid V-cycle possesses optimal convergence properties. Furthermore, through a series of numerical experiments we test the performance of the method for single-asset option problems. Throughout the paper we focus on models of European options.