This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Giles, M. B. Search for Related Content

Multilevel Monte Carlo Path Simulation

Oxford University Mathematical Institute, and Oxford—Man Institute of Quantitative Finance, Oxford OX1 3LB, United Kingdom
mike.giles{at}maths.ox.ac.uk

We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O() is reduced from O(^–3) to O(^–2 (log )²). The analysis is supported by numerical results showing significant computational savings.

Subject classifications: analysis of algorithms; computational complexity; finance; simulation; efficiency.
History: Received May 2006; revision received March 2007; accepted April 2007.