  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.
