Calibration in Finance: Very Fast Greeks Through Algorithmic Differentiation and Implicit Function

Abstract

Adjoint Algorithmic Differentiation is an efficient way to obtain price derivatives with respect to the data inputs. We describe how the process efficiency can be further improved when a model calibration is performed. Using the implicit function theorem, differentiating the numerical process used in calibration is not required. The resulting implementation is more efficient than automatic differentiation. The efficiency is described for root-finding and least square calibration.