# Mini-symposium on automatic differentiation and its applications in the financial industry

## TL;DR

This paper explores how automatic differentiation, especially Adjoint Algorithmic Differentiation (AAD), can enhance the computation of financial sensitivities, addressing recent regulatory demands and the complexity of financial models.

## Contribution

It provides an overview of applying automatic differentiation and AAD in financial contexts, highlighting the need for specialized tools and theoretical insights for complex derivatives and simulations.

## Key findings

- AAD improves accuracy of financial sensitivities
- Dedicated tools are needed for complex financial functions
- Automatic differentiation helps meet regulatory computation demands

## Abstract

Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic differentiation can be used. In between formal derivation and standard numerical schemes, this approach is based on software solutions applying mechanically the chain rule to obtain an exact value for the desired derivative. It has a cost in memory and cpu consumption. For participants of financial markets (banks, insurances, financial intermediaries, etc), computing derivatives is needed to obtain the sensitivity of its exposure to well-defined potential market moves. It is a way to understand variations of their balance sheets in specific cases. Since the 2008 crisis, regulation demand to compute this kind of exposure to many different case, to be sure market participants are aware and ready to face a wide spectrum of configurations. This paper shows how automatic differentiation provides a partial answer to this recent explosion of computation to perform. One part of the answer is a straightforward application of Adjoint Algorithmic Differentiation (AAD), but it is not enough. Since financial sensitivities involves specific functions and mix differentiation with Monte-Carlo simulations, dedicated tools and associated theoretical results are needed. We give here short introductions to typical cases arising when one use AAD on financial markets.