# Remarks on stochastic automatic adjoint differentiation and financial models calibration

## TL;DR

This paper examines the use of Automatic Adjoint Differentiation (AAD) for calibrating stochastic models, highlighting its SIMD parallelization capabilities and validating theoretical findings with numerical experiments.

## Contribution

It demonstrates the SIMD parallelization of AAD in stochastic model calibration and confirms the theoretical results through numerical experiments.

## Key findings

- AAD enables perfect SIMD parallelization in calibration tasks.
- Theoretical analysis aligns with numerical experiment results.
- Provides computational cost assessment for AAD in this context.

## Abstract

In this work, we discuss the Automatic Adjoint Differentiation (AAD) for functions of the form $G=\frac{1}{2}\sum_1^m (Ey_i-C_i)^2$, 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.}