Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation

Michael Giles*, Kristian Debrabant, Andreas Rößler

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The multilevel Monte Carlo path simulation method introduced by Giles (Operations Research, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milstein discretisation; this has an improved order of strong convergence compared to the standard Euler-Maruyama method, and it is proved that this leads to an improved order of convergence of the variance of the multilevel estimator. Numerical results are also given for basket options to illustrate the relevance of the analysis.

Original languageEnglish
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume24
Issue number8
Pages (from-to)3881-3903
ISSN1531-3492
DOIs
Publication statusPublished - 2019

Keywords

  • Computational finance
  • Monte Carlo
  • Multilevel
  • Numerical analysis
  • Stochastic differential equations

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