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Adjoint Algorithmic Differentiation and the Derivative of the Cholesky Decomposition

12 Pages Posted: 18 Dec 2015  

Paul Koerber

Belfius Bank, Market Validation

Date Written: December 15, 2015

Abstract

Adjoint Algorithmic Differentiation is an efficient method to calculate the sensitivities of financial instruments to the input parameters. It does require an implementation of the derivative of every elementary step in the pricing algorithm. In particular, for calculating correlation sensitivities in a Monte Carlo simulation it has been proposed to use a step-by-step adjoint derivative of the Cholesky factorization. In this paper we introduce a one-line matrix-level algorithm which uses only matrix inversion and multiplication and can thus be performed by a standard library for linear algebra. Moreover, it allows for a more time-efficient calculation of the standard errors on these sensitivities.

Keywords: Adjoint Algorithmic Differentiation, Monte Carlo, derivatives pricing, sensitivities, Cholesky decomposition

Suggested Citation

Koerber, Paul, Adjoint Algorithmic Differentiation and the Derivative of the Cholesky Decomposition (December 15, 2015). Available at SSRN: https://ssrn.com/abstract=2703893 or http://dx.doi.org/10.2139/ssrn.2703893

Paul Koerber (Contact Author)

Belfius Bank, Market Validation ( email )

Rogierplaats 11
Brussels, 1210
Belgium

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