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Double Kernel estimation of sensitivities

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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.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/41/64/49/PDF/ArticleDouble.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number hal-00416449.

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    Date of creation: Sep 2009
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    Publication status: Published, Journal of Applied Probability, 2009, 46, 3, ...
    Handle: RePEc:hal:journl:hal-00416449

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00416449/en/
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    Related research

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

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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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