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

摘要

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.