Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation

Michael B. Giles*, Kristian Debrabant, Andreas Rößler

*Korrespondierende/r Autor/-in für diese Arbeit
1 Zitat (Scopus)

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.

OriginalspracheEnglisch
ZeitschriftDiscrete and Continuous Dynamical Systems - Series B
Jahrgang24
Ausgabenummer8
Seiten (von - bis)3881-3903
Seitenumfang23
ISSN1531-3492
DOIs
PublikationsstatusVeröffentlicht - 08.2019

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