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Double Kernel Estimation of Sensitivities

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Date
2009
Link to item file
http://hal.archives-ouvertes.fr/hal-00416449/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
Nonparametric Regression; Monte Carlo Simulation; Sensitivity Estimation
Journal issue
Journal of Applied Probability
Volume
46
Number
3
Publication date
2009
Article pages
791-811
Publisher
Applied Probability Trust
DOI
http://dx.doi.org/10.1239/jap/1253279852
URI
https://basepub.dauphine.fr/handle/123456789/3493
Collections
  • CEREMADE : Publications
Metadata
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Author
Elie, Romuald
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

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