Remarks on stochastic automatic adjoint differentiation and financial models calibration

Abstract

In this work, we discuss the Automatic Adjoint Differentiation (AAD) for functions of the form $G=\frac{1}{2}{\sum }_1^m(E{y}_i-C_i{)}^2$, which often appear in the calibration of stochastic models. { We demonstrate that it allows a perfect SIMD\footnote{Single Input Multiple Data} parallelization and provide its relative computational cost. In addition we demonstrate that this theoretical result is in concordance with numeric experiments.}