Automatic Adjoint Differentiation for special functions involving expectations

Abstract

We explain how to compute gradients of functions of the form $G=\frac{1}{2}{\sum }_{i=1}^m(E{y}_i-C_i{)}^2$, which often appear in the calibration of stochastic models, using Automatic Adjoint Differentiation and parallelization. We expand on the work of arXiv:1901.04200 and give faster and easier to implement approaches. We also provide an implementation of our methods and apply the technique to calibrate European options.

16 pages, 1 figure, v2: added acknowledgement