Arbitrage-Free Bond and Yield Curve Forecasting with Neural Filters under HJM Constraints

ArXiv ID: 2511.17892 “View on arXiv”

Authors: Xiang Gao, Cody Hyndman

Abstract

We develop an arbitrage-free deep learning framework for yield curve and bond price forecasting based on the Heath-Jarrow-Morton (HJM) term-structure model and a dynamic Nelson-Siegel parameterization of forward rates. Our approach embeds a no-arbitrage drift restriction into a neural state-space architecture by combining Kalman, extended Kalman, and particle filters with recurrent neural networks (LSTM/CLSTM), and introduces an explicit arbitrage error regularization (AER) term during training. The model is applied to U.S. Treasury and corporate bond data, and its performance is evaluated for both yield-space and price-space predictions at 1-day and 5-day horizons. Empirically, arbitrage regularization leads to its strongest improvements at short maturities, particularly in 5-day-ahead forecasts, increasing market-consistency as measured by bid-ask hit rates and reducing dollar-denominated prediction errors.

Keywords: Heath-Jarrow-Morton (HJM), Nelson-Siegel, Arbitrage-Free, Neural State-Space, Recurrent Neural Networks (LSTM), Bonds

Complexity vs Empirical Score

  • Math Complexity: 9.2/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced mathematics, including the Heath-Jarrow-Morton framework, stochastic differential equations, Kalman/particle filters, and neural network integration with explicit arbitrage constraints, warranting a high complexity score. It also demonstrates strong empirical rigor with backtesting on U.S. Treasury and corporate bond data, measuring performance across horizons and maturities, and reporting metrics like bid-ask hit rates and dollar-denominated errors.
  flowchart TD
    A["Research Goal:<br>Arbitrage-Free Bond &<br>Yield Curve Forecasting"] --> B["Data & Inputs:<br>US Treasury & Corporate Bonds"]
    B --> C["Methodology:<br>Neural State-Space Model<br>with HJM Constraints"]
    C --> D["Computational Process:<br>LSTM/CLSTM + Kalman/Particle Filters"]
    D --> E["Training:<br>Arbitrage Error<br>Regularization AER"]
    E --> F["Key Findings:<br>Increased Accuracy<br>Bid-Ask Alignment<br>Short Maturity Improvement"]