Double Kernel estimation of sensitivities

Romuald Elie ()
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Romuald Elie: CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX

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Abstract: This paper adresses 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 been recently introduced by Elie, Fermanian and Touzi through a randomization of the parameter of interest combined with non parametric estimation techniques. This paper studies another type of those estimators whose interest is 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 little more stringent condition, its rate of convergence equals the one of those introduced by Elie, Fermanian and Touzi 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 type of estimators for sensitivities.

Keywords: Sensitivity estimation; Monte Carlo simulation; Non-parametric regression. (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-pke
Date: 2009-09
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00416449/en/
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Published, Journal of Applied Probability, 2009, 46, 3, ...

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Persistent link: http://EconPapers.repec.org/RePEc:hal:journl:hal-00416449_v1

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