Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities

Abstract

This dissertation explores a key challenge of the financial industry — the efficient computation of sensitivities of financial instruments. The adjoint approach to solving affine recursion problems (ARPs) is presented as a solution to this challenge. A Monte Carlo setting is adopted and it is illustrated how computational efficiency in sensitivity calculation may be significantly improved via the pathwise derivatives method through adapting an adjoint approach. This is achieved through the reversal of the order of differentiation in the pathwise derivatives algorithm in comparison to the standard, intuitive ‘forward’ approach. The Libor market model (LMM) framework is selected for examples to demonstrate these computational savings, with varying degrees of complexity of the LMM explored, from a one-factor model with constant volatility to a full factor model with time homogeneous volatilities.