Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage

2026-05-12

AI Summary

This study addresses the manifold collapse and arbitrage violations arising from the neglect of no-arbitrage constraints in deep learning–based term structure modeling. To this end, the authors propose a two-stage framework: first, a Student-t conditional variational autoencoder with dynamic level injection (CVAE-t+LS) extracts a robust heavy-tailed yield curve manifold, disentangling macroscopic shape from absolute interest rate levels; second, a neural stochastic differential equation (Neural SDE) equipped with embedded no-arbitrage partial differential equation constraints models the continuous-time evolution of latent variables. By integrating physics-informed constraints with deep generative modeling, the approach achieves an average term structure RMSE of 6.58 basis points across USD, GBP, and JPY sovereign bond markets—significantly outperforming classical HJM models—while effectively avoiding parallel shifts and violations of the zero lower bound, and enabling high-quality continuous-time scenario generation and macroeconomic state identification.

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.

Problem

• Yield Curves
• No-arbitrage
• Manifold Collapse
• Term Structure
• Deep Learning

Innovation

• Physics-informed generative model
• No-arbitrage PDE
• Neural SDE
• Conditional Variational Autoencoder
• Term structure manifold