Automatic Adjoint Differentiation for special functions involving expectations

TL;DR

This paper presents an improved method for computing gradients of expectation-based functions using Automatic Adjoint Differentiation, with applications to calibrating stochastic models and European options.

Contribution

It introduces faster, easier-to-implement approaches for automatic differentiation of functions involving expectations, expanding on previous work.

Findings

Enhanced gradient computation speed and simplicity

Successful application to European option calibration

Implementation available for practical use

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.