Multilevel Richardson–Romberg extrapolation

We propose and analyze a Multilevel Richardson-Romberg (MLRR) estimator which com-bines the higher order bias cancellation of the Multistep Richardson-Romberg (MSRR) method introduced in [Pag07] and the variance control resulting from the stratification in the Multilevel Monte Carlo (MLMC) method (see [Hei01]). 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 of Yh can be expanded at any order in h. We analyze and compare these estimators on two numerical problems: the classical vanilla option pricing by MC simulation and the less classica