An introduction to multilevel Monte Carlo for option valuation

Desmond J. Higham

Research output: Contribution to journalArticle

5 Citations (Scopus)
176 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)2347-2360
Number of pages14
JournalInternational Journal of Computer Mathematics
Volume92
Issue number12
Early online date26 Aug 2015
DOIs
Publication statusPublished - 11 Sep 2015

Keywords

  • computational complexity
  • control variate
  • Euler–Maruyama
  • Monte Carlo
  • option value
  • stochastic differential equation
  • variance reduction

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