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Double Kernel Estimation of Sensitivities

Part of: Nonparametric inference Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  14 July 2016

Romuald Elie
Romuald Elie*
Affiliation:
Université Paris-Dauphine and CREST
*
∗Postal address: CEREMADE, CNRS UMR 7534, Université Paris-Dauphine, Place du Marechal de Lattre de Tassigny, 75775 Paris Cedex 16, France. Email address: elie@ensae.fr
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Abstract

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In this paper we address the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance, for example, the sensitivities of the price of a contingent claim are called the Greeks. A new way of estimating the Greeks has recently been introduced in Elie, Fermanian and Touzi (2007) through a randomization of the parameter of interest combined with nonparametric estimation techniques. In this paper we study another type of estimator that turns out to be closely related to the score function, which is well known to be the optimal Greek weight. This estimator relies on the use of two distinct kernel functions and the main interest of this paper is to provide its asymptotic properties. Under a slightly more stringent condition, its rate of convergence is the same as the one of the estimator introduced in Elie, Fermanian and Touzi (2007) and outperforms the finite differences estimator. In addition to the technical interest of the proofs, this result is very encouraging in the dynamic of creating new types of estimator for the sensitivities.

Keywords

Sensitivity estimationMonte Carlo simulationnonparametric regression

MSC classification

Secondary: 62G08: Nonparametric regression 11K45: Pseudo-random numbers; Monte Carlo methods
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 3 , September 2009 , pp. 791 - 811
Copyright
Copyright © Applied Probability Trust 2009 

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