Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage

TL;DR

This paper presents a physics-informed deep learning framework for modeling yield curves that respects no-arbitrage constraints, improves forecasting accuracy, and detects macroeconomic regimes.

Contribution

It introduces a novel two-stage architecture combining a Student-t CVAE with a neural SDE penalized by a no-arbitrage PDE, addressing arbitrage violations in yield curve modeling.

Findings

Reduces out-of-sample forecasting error to 6.58 bps RMSE.

Overcomes arbitrage violations and zero-lower-bound issues in extreme environments.

Enables unsupervised macroeconomic regime detection.

Abstract

This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling. We demonstrate that standard generative models and unconstrained statistical extrapolations suffer from "manifold collapse" and severe arbitrage violations when forecasting term structures across diverse macroeconomic regimes. To overcome this, we propose a two-stage architecture. First, a Student-t Conditional Variational Autoencoder with Dynamic Level Injection (CVAEsT+LS) extracts a robust, heavy-tailed term structure manifold, effectively decoupling macroeconomic shape dynamics from absolute base rates. Second, the latent dynamic evolution is governed by a continuous-time Neural Stochastic Differential Equation (SDE) strictly penalized by a No-Arbitrage Partial Differential Equation (PDE). Empirical results across multiple sovereign currencies (USD, GBP, JPY) confirm that our synergistic approach drastically reduces out-of-sample forecasting errors -- achieving an exceptional 6.58 bps Mean Tenor RMSE -- and successfully overcomes the massive parallel drift and zero-lower-bound violations exhibited by the classical HJM model in extreme environments. Furthermore, through phase space vector field analysis, we demonstrate the model's superior capability in unsupervised macroeconomic regime detection and high-quality continuous-time scenario generation. Ultimately, this research provides a highly scalable, mathematically sound evolutionary engine for term structure modeling.