In quantitative finance, automatic differentiation is commonly used to efficiently compute price sensitivities. See Homescu (2011) for a general introduction and overview. I recently started to look into it with two different applications in mind: i) computation of moments from characteristic functions and ii) computation of implied densities from parametric volatility smiles. In this post, I provide a short introduction into computing general order derivatives with CppAD in forward mode.
Automatic Differentiation with CppAD