Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage

2026-05-14 · Source: stat.ML updates on arXiv.org · Field: Finance & Economics — Capital Markets & Investment Management, FinTech & Digital Financial Services, Economic Analysis & Policy · Depth: Expert, extended

Summary

This paper introduces a physics-informed generative framework that resolves the conflict between deep learning's statistical flexibility and fixed-income modeling's theoretical constraints. The proposed two-stage architecture, a Student-t Conditional Variational Autoencoder with Dynamic Level Injection (CVAE_sT+LS), extracts a robust, heavy-tailed term structure manifold by decoupling macroeconomic shape dynamics from absolute base rates. Subsequently, a continuous-time Neural Stochastic Differential Equation (SDE) governs latent dynamics, strictly penalized by a No-Arbitrage Partial Differential Equation (PDE). Empirical results across USD, GBP, and JPY sovereign currencies demonstrate that this approach drastically reduces out-of-sample forecasting errors to an exceptional 6.58 bps Mean Tenor RMSE. The model successfully overcomes massive parallel drift and zero-lower-bound violations seen in classical HJM models, offering superior unsupervised macroeconomic regime detection and high-quality continuous-time scenario generation.

Key takeaway

For research scientists developing advanced fixed-income models, this framework offers a robust solution to the long-standing challenge of integrating deep learning with no-arbitrage constraints. You should consider adopting a two-stage approach that explicitly decouples yield curve levels from shapes and incorporates heavy-tailed distributions. This will enhance model stability and accuracy, particularly in volatile or extreme macroeconomic environments, ensuring compliance with fundamental financial laws.

Key insights

A physics-informed generative model forecasts yield curves with high accuracy and no-arbitrage compliance.

Principles

• Decouple macroeconomic shape from base rates.
• Use heavy-tailed distributions for market shocks.
• Enforce no-arbitrage via PDE constraints.

Method

A two-stage architecture: CVAE_sT+LS for manifold learning and a Neural SDE with a No-Arbitrage PDE penalty for continuous-time dynamics, optimizing a composite loss function.

In practice

• Achieves 6.58 bps Mean Tenor RMSE in forecasting.
• Detects macroeconomic regimes unsupervised.
• Generates continuous-time financial scenarios.

Topics

• Yield Curve Modeling
• Variational Autoencoders
• No-Arbitrage Constraints
• Neural Stochastic Differential Equations
• Student-t Distribution

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.