A multigrid preconditioner for an adaptive Black-Scholes solver

Alison Ramage, L. von Sydow

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper is concerned with the efficient solution of the linear systems of equations that arise from an adaptive space-implicit time discretisation of the Black-Scholes equation. These nonsymmetric systems are very large and sparse, so an iterative method will usually be the method of choice. However, such a method may require a large number of iterations to converge, particularly when the timestep used is large (which is often the case towards the end of a simulation which uses adaptive timestepping). An appropriate preconditioner is therefore desirable. In this paper we show that a very simple multigrid algorithm with standard components works well as a preconditioner for these problems. We analyse the eigenvalue spectrum of the multigrid iteration matrix for uniform grid problems and illustrate the method’s efficiency in practice by considering the results of numerical experiments on both uniform grids and those which use adaptivity in space.
Original languageEnglish
Pages (from-to)217-233
Number of pages17
JournalBIT Numerical Mathematics
Volume51
Issue number1
DOIs
Publication statusPublished - Jan 2011

Keywords

  • mathematics
  • Black-Scholes
  • equations
  • preconditioning
  • option pricing
  • multigrid

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