Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage

Paper: arXiv 2605.12764

Authors: Fusheng Luo, H’elyette Geman

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated approach using variational autoencoders and neural SDEs, achieving high complexity and empirical rigor. The novelty lies in addressing manifold collapse and arbitrage violations in term structure modeling. The overall quality is strong.

Research Flowchart

  flowchart TD
    A[Research Goal: Physics-informed generative framework for term structure modeling] --> B[Key Methodology: Two-stage architecture]
    B --> C[1. Student-t CVAE + Dynamic Level Injection (CVAEsT+LS)]
    B --> D[2. Neural SDE penalized by No-Arbitrage PDE]
    C --> E[Data/Inputs: Historical sovereign currency yields (USD, GBP, JPY) across macroeconomic regimes]
    D --> F[Computational Processes: Extract heavy-tailed manifold; evolve latent dynamics; enforce no-arbitrage]
    E --> F
    F --> G[Key Findings: 6.58 bps Mean Tenor RMSE; eliminates zero-lower-bound violations; superior regime detection & scenario generation]

Cited References (32)

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5. Forecasting the term structure of government bond yields (2006)
6. Consistency problems for Heath-Jarrow-Morton interest rate models (2001)
7. Hyperspherical variational auto-encoders (2018) — link
8. Student-t Variational Autoencoder for Robust Density Estimation. (2018)

0 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.