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Rapport Année : 2014

Multilevel Richardson-Romberg extrapolation

Résumé

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 [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 $\varepsilon$ 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 $\esp{Y_h}-\esp{Y_0}$ 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.
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Dates et versions

hal-00920660 , version 1 (19-12-2013)
hal-00920660 , version 2 (30-04-2014)
hal-00920660 , version 3 (19-12-2014)

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  • HAL Id : hal-00920660 , version 2

Citer

Vincent Lemaire, Gilles Pagès. Multilevel Richardson-Romberg extrapolation. 2014. ⟨hal-00920660v2⟩
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