The Annals of Applied Probability

Central limit theorem for the multilevel Monte Carlo Euler method

Mohamed Ben Alaya and Ahmed Kebaier

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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.

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Ann. Appl. Probab. Volume 25, Number 1 (2015), 211-234.

First available in Project Euclid: 16 December 2014

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 62F12: Asymptotic properties of estimators 65C05: Monte Carlo methods 60H35: Computational methods for stochastic equations [See also 65C30]

Central limit theorem multilevel Monte Carlo methods Euler scheme finance


Ben Alaya, Mohamed; Kebaier, Ahmed. Central limit theorem for the multilevel Monte Carlo Euler method. Ann. Appl. Probab. 25 (2015), no. 1, 211--234. doi:10.1214/13-AAP993.

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