Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance

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. AAD can be applied in conjunction with any analytical or numerical method (finite difference, Monte Carlo, etc) used for pricing, preserving the numerical properties of the original method. Examples and a literature survey are included