Double kernel estimation of sensitivities
Elie Romuald
Source: J. Appl. Probab.
Volume 46, Number 3
(2009), 791-811.
Abstract
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.
Primary Subjects: 62G08
Secondary Subjects: 11K45
Keywords: Sensitivity estimation; Monte Carlo simulation; nonparametric regression
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1253279852
Digital Object Identifier: doi:10.1239/jap/1253279852
Zentralblatt MATH identifier:
05611418
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