Efficient Pricing and Greeks in the Cross-Currency LIBOR Market Model

Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance

“…It is our experience [47]that the discrete adjoint can still be applied for cases such gradient doe not exist; in those cases the numerical adjoint code will provide us not the gradient, but rather subgradients. Consequently, one will have to employ optimization algorithms that are especially designed to use subgradients instead of gradient 8 Computational finance literature on adjoint and AD In the last several years quite a few papers were added to the literature on adjoint/AD applied to computational finance [11,22,20,21,24,23,32,30,31,41,50,48,49,54,52,55,56,65,3,9,18,67] . For selected papers we give an overview in the following sections…”

“…In the framework of the cross-currency displaced-diffusion LIBOR market model, [11] employs adjoint techniques to compute Greeks for two commonly traded cross-currency exotic interest rate derivatives: cross-currency swaps (CCS) and power reverse dual currency (PRDC) swaps. They measure the computational times relative to the basic implementation of the crosscurrency LIBOR market model, that is with standard least squares regression used to compute the exercise strategy.…”