'Bernoulli Society for Mathematical Statistics and Probability'
Doi
Abstract
International audienceWe propose and analyze a Multilevel Richardson-Romberg (MLRR) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg (MSRR) method introduced in [Pages 07] and the variance control resulting from the stratification in the Multilevel Monte Carlo (MLMC) method (see [Heinrich, 01] and [Giles, 08]). Thus we show that in standard frameworks like discretization schemes of diffusion processes an assigned quadratic error ε can be obtained with our (MLRR) estimator with a global complexity of log(1/ε)/ε2 instead of (log(1/ε))2/ε2 with the standard (MLMC) method, at least when the weak error E[Yh]−E[Y0] of the biased implemented estimator Yh can be expanded at any order in h. We analyze and compare these estimators on two numerical problems: the classical vanilla and exotic option pricing by Monte Carlo simulation and the less classical Nested Monte Carlo simulation
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