Let f be a regular, locally Lipschitz real-valued function defined on an open convex subset of a normed space. We show that at any unit direction u, the upper second ...

The FD= and FDHESSIAN= options specify the use of finite difference approximations of the derivatives. The FD= option specifies that all derivatives are approximated using function evaluations, and ...

This paper deals with the computation of second-order or higher Greeks of financial securities. It combines two methods, vibrato and automatic differentiation (AD), and compares these with other ...

First-order derivatives: n additional function calls are needed. Second-order derivatives based on gradient calls, when the "grd" module is specified (Dennis and Schnabel 1983): n additional gradient ...