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

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.