Deep Learning in a Generalized HJM-type Framework Through Arbitrage-Free Regularization

TL;DR

This paper presents a deep learning-based method for selecting arbitrage-free HJM-type models that closely approximate given factor models, ensuring no arbitrage opportunities in bond markets.

Contribution

It introduces a novel regularization approach for arbitrage-free model selection using deep learning, with a tractable penalty formulation in affine-term structure models.

Findings

Effective deep-learning approach for arbitrage-free bond modeling

Numerical results demonstrate improved model accuracy

Penalty terms successfully enforce no-arbitrage conditions

Abstract

We introduce a regularization approach to arbitrage-free factor-model selection. The considered model selection problem seeks to learn the closest arbitrage-free HJM-type model to any prespecified factor-model. An asymptotic solution to this, a priori computationally intractable, problem is represented as the limit of a 1-parameter family of optimizers to computationally tractable model selection tasks. Each of these simplified model-selection tasks seeks to learn the most similar model, to the prescribed factor-model, subject to a penalty detecting when the reference measure is a local martingale-measure for the entire underlying financial market. A simple expression for the penalty terms is obtained in the bond market withing the affine-term structure setting, and it is used to formulate a deep-learning approach to arbitrage-free affine term-structure modelling. Numerical implementations are also performed to evaluate the performance in the bond market.