Modifications to a classic BFGS library for use with SIMD-equipped hardware and an AAD library

TL;DR

This paper presents modifications to the BFGS optimization method and a corresponding library that leverage SIMD and automatic differentiation to significantly improve performance on non-parallelizable functions, demonstrated through financial calibration examples.

Contribution

The authors introduce a modified BFGS method and an enhanced LBFGS++ library that utilize SIMD and AAD, providing automatic interface integration for improved optimization performance.

Findings

Up to 3.8 times faster calibration of European Swaption curves.

1.4 times faster calibration of LMM models.

Effective use of SIMD and AAD in non-parallelizable functions.

Abstract

We introduce certain modifications of the BFGS method for functions that are not parallelizable by nature (having consecutive operations only) taking advantage of SIMD. We also provide a modified LBFGS\texttt{++} library that takes advantage of these modifications, and the use of AAD, and give an interface for AAD users that takes advantage of the modified library automatically. We give two examples to illustrate the performance. The modified library is up to 3.8 times faster for European Swaption curve calibration in ORE (not parallelizable) and 1.4 times faster for calibrating the LMM model by a set of European options.