Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance

TL;DR

This paper reviews adjoint and automatic differentiation techniques for efficiently computing sensitivities in computational finance, highlighting their advantages over finite difference methods in terms of accuracy and computational cost.

Contribution

It provides an overview and comparison of adjoint and AD methods for sensitivities, including examples and a literature survey, emphasizing their benefits in finance applications.

Findings

AD methods can reduce computation time significantly.

Sensitivities computed by AD are accurate up to machine precision.

The paper includes practical examples and a comprehensive literature review.

Abstract

Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic differentiation, techniques to calculate these sensitivities. When compared to finite difference approximation, this approach can potentially reduce the computational cost by several orders of magnitude, with sensitivities accurate up to machine precision. Examples and a literature survey are also provided.