Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem

Abstract

Adjoint Algorithmic Differentiation is an efficient way to obtain financial instrument price derivatives with respect to the data inputs. Often the differentiation does not cover the full pricing process when a model calibration is performed. Thanks to the implicit function theorem, the differentiation of the solver embedded in the calibration is not required to differentiate to full pricing process. An efficient approach to the full process differentiation is described.

Keywords: Financial model calibration, adjoint algorithmic differentiation, implicit function theorem, equation solver, efficient derivatives computation