Deep Learning in a Generalized HJM-type Framework Through Arbitrage-Free Regularization
This work addresses the challenge of ensuring arbitrage-free models in financial pricing, which is crucial for practitioners in quantitative finance, though it appears incremental as it builds on existing HJM-type frameworks.
The authors tackled the problem of learning arbitrage-free factor models in finance by introducing a regularization approach that penalizes deviations from arbitrage-free conditions, with numerical implementations in bond markets showing performance improvements.
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.