TY - JOUR
T1 - Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation
AU - Giles, Michael B.
AU - Debrabant, Kristian
AU - Rößler, Andreas
N1 - Publisher Copyright:
© 2019 American Institute of Mathematical Sciences. All rights reserved.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/8
Y1 - 2019/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85072575012&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2018335
DO - 10.3934/dcdsb.2018335
M3 - Journal articles
AN - SCOPUS:85072575012
SN - 1531-3492
VL - 24
SP - 3881
EP - 3903
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 8
ER -