Double Kernel estimation of sensitivities

TL;DR

This paper introduces a new double kernel estimator for sensitivities (Greeks) in finance, analyzing its asymptotic properties and demonstrating its superior convergence rate over finite differences methods.

Contribution

It proposes a novel double kernel estimator for sensitivities, providing its asymptotic analysis and showing improved convergence compared to existing methods.

Findings

Estimator has the same convergence rate as recent methods.

Outperforms finite differences estimator in asymptotic efficiency.

Provides theoretical foundation for new sensitivity estimation techniques.

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.