Algorithmic Adjoint Differentiation (AAD) for Swap Pricing and DV01 Risk

We present Algorithmic Adjoint Differentiation (AAD), also known as Automatic Adjoint Differentiation, which computes the derivative(s) of computer code. In finance this leads to a relatively new and novel approach, pioneered by (Giles and Glasserman, 2006), to compute financial risks. When trading in electronic rates markets, AD can be used to produce exact swap risks, such as DV01, at high speed and give users a competitive advantage (Burgess 2021a).AD is well presented in finance, see (Capriotti, 2010), (NAG, n.d.) and (Savine, 2018). However, in what follows we present algorithmic differentiation from an implementation perspective with a focus on how to apply AAD to interest rate swaps (IRS) for interest rate risk (DV01) calculations. Firstly, we give a brief overview of interest rate swaps and how to price them. Secondly we discuss swap risks, PV01 and DV01 risk calculations and the different approaches on how to compute them, namely via analytical closed-form solutions, numerical bumping and curve Jacobians. Thirdly we introduce algorithmic differentiation (AD) and show how to implement AD in both tangent and adjoint modes on a simple function. Fourthly we show how to compute DV01 risk using AD for an interest rate swap. Fifthly we discuss how to professionally implement AD using both open-source and commercial software solutions.Throughout this implementation paper we present AD case studies in C++ code, for a simple function and for swaps. The source code has also been pre-loaded onto a free online compiler and can be run with a single button click, see the code footnotes for details. Furthermore, the raw source code is available at https://github.com/nburgessx/Papers/tree/main/SwapAD