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This paper adresses the general issue of estimating the sensitivity of theexpectation of a random variable with respect to a parameter characterizing itsevolution. In finance for example, the sensitivities of the price of acontingent claim are called the Greeks. A new way of estimating the Greeks hasbeen recently introduced by Elie, Fermanian and Touzi through a randomizationof the parameter of interest combined with non parametric estimationtechniques. This paper studies another type of those estimators whose interestis to be closely related to the score function, which is well known to be theoptimal Greek weight. This estimator relies on the use of two distinct kernelfunctions and the main interest of this paper is to provide its asymptoticproperties. Under a little more stringent condition, its rate of convergenceequals the one of those introduced by Elie, Fermanian and Touzi and outperformsthe finite differences estimator. In addition to the technical interest of theproofs, this result is very encouraging in the dynamic of creating new type ofestimators for sensitivities.

Double Kernel estimation of sensitivities