Before revision:  This methodology is compared in terms of accuracy, efficiency, and implementation /maintenance costs with common techniques used for the same purpose, such as amortisation-based, regression-based and Adjoint Algorithmic Differentiation. Measured in terms of these criteria, the methodologies based on Chebyshev interpolants offer an optimal solution and set a new benchmark standard for the industry0pt%DIFAUXCMD ) and Deep Neural Nets (\mbox{%DIFAUXCMD DNNs IM}0pt%DIFAUXCMD )} .
After revision:  This methodology is compared in terms of accuracy, speed and implementation efforts obtained, compared to the benchmark (DIM obtained calling pricing functions such as are found in risk engines), are better than those obtained by alternative methods presented in the literature, such as regressions (\mbox{%DIFAUXCMD Zhu Chan0pt%DIFAUXCMD ) and Deep Neural Nets (\mbox{%DIFAUXCMD DNNs IM}0pt%DIFAUXCMD )} .