Computational concerns, the ability to calculate values and risks of derivatives portfolios practically and in reasonable time, have always been a major part of quantitative finance. With the rise of bank-wide regulatory simulations like CVA and capital requirements, it became a matter of survival. Modern computational finance makes the difference between calculating CVA risk overnight in large data centers and praying that they complete by morning, or in real-time, within minutes on a workstation.

Computational finance became a key skill, now expected from all quantitative analysts, developers, risk professionals, and anyone involved with financial derivatives. It is increasingly taught in masters programs in finance, such as the Copenhagen University's MSc Mathematics - Economics, where this publication is the curriculum in numerical finance.

Danske Bank's quantitative research built its front office and regulatory systems combining technologies such as model hierarchies, scripting of transactions, parallel Monte-Carlo, a special application of regression proxies, and Automatic Adjoint Differentiation (AAD).

In 2015, Danske Bank demonstrated the computation of a sizeable CVA on a laptop in seconds, and its full market risk in minutes, without loss of accuracy, and won the In-House System of the Year Risk award.

Wiley's Computational Finance series, written by some of the very people who wrote Danske Bank's systems, offers a unique insight into the modern implementation of financial models. The volumes combine financial modeling, mathematics, and programming to resolve real-life financial problems and produce effective derivatives software.

The scientific, financial, and programming notions are developed in a pedagogical, self-contained manner. The publications are inseparable from the professional source code in C++ that comes with them. The books build the libraries step by step and the code demonstrates the practical application of the concepts discussed in the publications.

This is an essential reading for developers and analysts, risk managers, and all professionals involved with financial derivatives, as well as students and teachers in Masters and PhD programs in finance.

ALGORITHMIC ADJOINT DIFFERENTIATION

This volume is written by Antoine Savine, who co-wrote Danske Bank's parallel simulation and AAD engines, and teaches volatility and computational finance in Copenhagen University's MSc Mathematics - Economics.

Arguably the strongest addition to numerical finance of the past decade, Algorithmic Adjoint Differentiation (AAD) is the technology implemented in modern financial software to produce thousands of accurate risk sensitivities within seconds on light hardware. AAD is one of the greatest algorithms of the 20th century. It is also notoriously hard to learn.

This book offers a one-stop learning and reference resource for AAD, its practical implementation in C++, and its application in finance. AAD is explained step by step across chapters that gently lead readers from the theoretical foundations to the most delicate areas of an efficient implementation, such as memory management, parallel implementation, and acceleration with expression templates.

The publication comes with a self-contained, complete, general-purpose implementation of AAD in standard modern C++. The AAD library builds on the latest advances in AAD research to achieve remarkable speed. The code is incrementally built throughout the publication, where all the implementation details are explained.

The publication also covers the application of AAD to financial derivatives and the design of generic, parallel simulation libraries. Readers with working knowledge of derivatives and C++ will benefit most, although the book does cover modern and parallel C++.

The book comes with a professional parallel simulation library in C++, connected to AAD. Some of the most delicate applications of AAD to finance, such as the differentiation through calibration, are also explained in words, mathematics, and code.