dc.contributor.author Touzi, Nizar dc.contributor.author Fermanian, Jean-David dc.contributor.author Elie, Romuald dc.date.accessioned 2009-06-19T08:50:22Z dc.date.available 2009-06-19T08:50:22Z dc.date.issued 2007 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/364 dc.language.iso en en dc.subject Greek weights; Monte Carlo simulation; nonparametric regression en dc.subject.ddc 519 en dc.title Kernel estimation of Greek weights by parameter randomization en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Ecole Nationale de la Statistique et de l'Administration Economique;France dc.description.abstracten A Greek weight associated to a parameterized random variable Z(λ) is a random variable π such that ∇λE[φ(Z(λ))]=E[φ(Z(λ))π] for any function φ. The importance of the set of Greek weights for the purpose of Monte Carlo simulations has been highlighted in the recent literature. Our main concern in this paper is to devise methods which produce the optimal weight, which is well known to be given by the score, in a general context where the density of Z(λ) is not explicitly known. To do this, we randomize the parameter λ by introducing an a priori distribution, and we use classical kernel estimation techniques in order to estimate the score function. By an integration by parts argument on the limit of this first kernel estimator, we define an alternative simpler kernel-based estimator which turns out to be closely related to the partial gradient of the kernel-based estimator of $\mathbb{E}[\phi(Z(\lambda))]$. Similarly to the finite differences technique, and unlike the so-called Malliavin method, our estimators are biased, but their implementation does not require any advanced mathematical calculation. We provide an asymptotic analysis of the mean squared error of these estimators, as well as their asymptotic distributions. For a discontinuous payoff function, the kernel estimator outperforms the classical finite differences one in terms of the asymptotic rate of convergence. This result is confirmed by our numerical experiments. en dc.relation.isversionofjnlname The Annals of Applied Probability dc.relation.isversionofjnlvol 17 en dc.relation.isversionofjnlissue 4 en dc.relation.isversionofjnldate 2007-11 dc.relation.isversionofjnlpages 1399 - 1423 en dc.relation.isversionofdoi http://dx.doi.org/10.1214/105051607000000186 en dc.description.sponsorshipprivate oui en dc.subject.ddclabel Probabilités et mathématiques appliquées en
﻿

## Files in this item

FilesSizeFormatView

There are no files associated with this item.