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Ben Alaya, Mohamed; Kebaier, Ahmed

Central limit theorem for the multilevel Monte Carlo Euler method. (English) Zbl 1320.60073

Ann. Appl. Probab. 25, No. 1, 211-234 (2015).
The multilevel Monte Carlo method for the computation of quantities \(\mathbb E[f(X_T)]\), where \((X_t)_{0\leq t \leq T}\) is a diffusion process and \(f\) some function (e.g. to price options), yields a remarkable reduction of the complexity in contrast to crude Monte Carlo algorithms. In this paper, the authors derive a central limit theorem of Lindeberg-Feller type for the multilevel Monte Carlo Euler scheme. The main tool is a stable law convergence theorem for the Euler scheme error of two consecutive levels of the multilevel algorithm. This result gives a precise description for the choice of the parameters to run the multilevel Monte Carlo Euler scheme. The explicitly characterized limiting variance in the central limit theorem allows to construct more accurate confidence intervals. A complexity analysis confirms the efficiency of the multilevel method. Moreover, a Berry-Esseen type bound is established.
Reviewer: Peter Parczewski (Mannheim)

Cited in 21 Documents

MSC:

60F05 Central limit and other weak theorems
65C05 Monte Carlo methods
62F12 Asymptotic properties of parametric estimators
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)

Keywords:

central limit theorem; multilevel Monte Carlo methods; Euler scheme
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References:

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