• DOI:10.3150/16-BEJ822
• Corpus ID: 28015292

Multilevel Richardson-Romberg Extrapolation

@article{Lemaire2014MultilevelRE,
  title={Multilevel Richardson-Romberg Extrapolation},
  author={Vincent Lemaire and Gilles Pag{\`e}s},
  journal={Derivatives eJournal},
  year={2014}
}

• V. Lemaire, G. Pagès
• Published 6 January 2014
• Mathematics
• Derivatives eJournal

We 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 [Pag07] and the variance control resulting from the stratification in the Multilevel Monte Carlo ($MLMC$) method (see [Hei01, Gil08]). Thus we show that in standard frameworks like discretization schemes of diffusion processes an assigned quadratic error $\varepsilon$ can be obtained with our ($MLRR$) estimator with a global complexity of $\log(1/\varepsilon)/\varepsilon^2$ instead of $(\log(1/\varepsilon))^2/\varepsilon^2$ with the standard ($MLMC$) method, at least when the weak error $\mathbf{E}[Y_h]-\mathbf{E}[Y_0]$ of the biased implemented estimator $Y_h$ 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.