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Double Kernel estimation of sensitivities

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  • Romuald Elie

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Romuald Elie, 2009. "Double Kernel estimation of sensitivities," Post-Print hal-00416449, HAL.
    • Handle: RePEc:hal:journl:hal-00416449
    Note: View the original document on HAL open archive server: https://hal.science/hal-00416449
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    References listed on IDEAS

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    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    2. Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Asymptotic Properties of Monte Carlo Estimators of Derivatives," Management Science, INFORMS, vol. 51(11), pages 1657-1675, November.
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    Keywords

    Sensitivity estimation; Monte Carlo simulation; Non-parametric regression.; Non-parametric regression;
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