Central limit theorem for the multilevel Monte Carlo Euler method

Abstract

This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central limit theorem of Lindeberg-Feller type for the multilevel Monte Carlo method associated with the Euler discretization scheme. To do so, we prove first a stable law convergence theorem, in the spirit of Jacod and Protter [Ann. Probab. 26 (1998) 267-307], for the Euler scheme error on two consecutive levels of the algorithm. This leads to an accurate description of the optimal choice of parameters and to an explicit characterization of the limiting variance in the central limit theorem of the algorithm. A complexity of the multilevel Monte Carlo algorithm is carried out.

Published in at http://dx.doi.org/10.1214/13-AAP993 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correction
• Statistical Romberg extrapolation: A new variance reduction method and applications to option pricing
• Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations

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