An introduction to multilevel Monte Carlo for option valuation

Higham, Desmond J. (2015) An introduction to multilevel Monte Carlo for option valuation. International Journal of Computer Mathematics, 92 (12). pp. 2347-2360. ISSN 0020-7160

[img]
Preview
Text (Higham-IJCM-2015-An-introduction-to-multilevel-Monte-Carlo-for)
Higham_IJCM_2015_An_introduction_to_multilevel_Monte_Carlo_for.pdf
Accepted Author Manuscript

Download (331kB)| Preview

    Abstract

    Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers a speed up of Ο(ε-1), where ε is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The 'multilevel philosophy' has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.