Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation

Journal article

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.

Files:: arXiv.pdf

(Preview, Accepted manuscript, pdf, 393.2KB, Terms of use)

Publisher:: American Institute of Mathematical Sciences
Journal:: Discrete and Continuous Dynamical Systems - Series B More from this journal
Volume:: 24
Issue:: 8
Pages:: 3881-3903
Publication date:: 2019-01-04
Acceptance date:: 2018-08-25
DOI:: 10.3934/dcdsb.2018335
EISSN:: 1553-524X
ISSN:: 1531-3492

Keywords:: Monte Carlo

computational finance

numerical analysis

stochastic differential equations

multilevel
Pubs id:: pubs:911639
UUID:: uuid:726fab5a-8c92-4b9e-9eeb-3ba7010607c7
Local pid:: pubs:911639
Source identifiers:: 911639
Deposit date:: 2018-09-01
ARK identifier:: ark:/29072/ora_726fab5a8c924b9e9eeb3ba7010607c7

Copyright holder:: American Institute of Mathematical Sciences
Notes:: Copyright © 2019 American Institute of Mathematical Sciences. This is the accepted manuscript version of the article. The final version is available online from the American Institute of Mathematical Sciences at: https://doi.org/10.3934/dcdsb.2018335

Licence:: Terms and Conditions of Use for Oxford University Research Archive

If you are the owner of this record, you can report an update to it here: Report update to this record