Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Xiang Gao, Cody Hyndman

TL;DR

This paper addresses the tension between economic consistency and predictive accuracy in fixed-income forecasting by embedding no-arbitrage constraints into a neural, filter-based framework grounded in the HJM forward-rate model and a dynamic Nelson–Siegel specification. An arbitrage-regularization penalty, $\Lambda^{(p)}$, is trained alongside a neural encoder that parameterizes time-varying factors $(\kappa_t,\theta_t,\sigma_t)$ and latent state $X_t$, using Kalman, extended Kalman, and particle filters to forecast yields and bond prices. Empirically, arbitrage-regularized forecasts improve market-consistency and short-horizon accuracy, with the strongest gains at 5 days and short maturities, particularly in yield-space (KF); price-space forecasts (EKF/PF) show more modest improvements but benefit from robust error modeling via a multivariate generalized Gaussian. The framework bridges classical term-structure theory with neural encoders and differentiable filters, offering a scalable, arbitrage-consistent approach for day-to-day pricing and risk management, with future extensions to jumps, macro factors, and KalmanNet-style filtering.

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.

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

TL;DR

This paper addresses the tension between economic consistency and predictive accuracy in fixed-income forecasting by embedding no-arbitrage constraints into a neural, filter-based framework grounded in the HJM forward-rate model and a dynamic Nelson–Siegel specification. An arbitrage-regularization penalty, , is trained alongside a neural encoder that parameterizes time-varying factors and latent state , using Kalman, extended Kalman, and particle filters to forecast yields and bond prices. Empirically, arbitrage-regularized forecasts improve market-consistency and short-horizon accuracy, with the strongest gains at 5 days and short maturities, particularly in yield-space (KF); price-space forecasts (EKF/PF) show more modest improvements but benefit from robust error modeling via a multivariate generalized Gaussian. The framework bridges classical term-structure theory with neural encoders and differentiable filters, offering a scalable, arbitrage-consistent approach for day-to-day pricing and risk management, with future extensions to jumps, macro factors, and KalmanNet-style filtering.

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.

Paper Structure

This paper contains 33 sections, 2 theorems, 63 equations, 17 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Contributions:
  3. Organization:
  4. Arbitrage-free pricing framework
  5. HJM forward rate model
  6. Dynamic Nelson-Siegel term structure
  7. Data and estimation result
  8. Forecasting framework
  9. Yield forecasting using the Kalman filter
  10. Price forecasting using the extended Kalman filter
  11. Price forecasting using the particle filter
  12. Dynamic parameterization by Recurrent Neural Networks
  13. Input layer
  14. Yield-space (linear) model.
  15. Price-space (nonlinear) model.
  16. ...and 18 more sections

Key Result

Theorem 2.1

Suppose the forward rate model has an affine structure given by $f(t,\tau) = \beta_\tau X_t$ and a mean-reverting state variable defined by where $\beta_\tau\in\mathbb{R}^{1\times d}$, $X_t\in\mathbb{R}^{d\times1}$, $\kappa_t\left(X_t\right):\mathbb{R}^{d\times1} \rightarrow \mathbb{R}^{d\times d}$, $\theta_t\left(X_t\right):\mathbb{R}^{d\times1} \rightarrow\mathbb{R}^{d\times 1}$, and $\sigma_t\

Figures (17)

  • Figure 2.1: Treasury yield curves from 2017 to 2019
  • Figure 2.2: State variables of Treasury from 2017 to 2019
  • Figure 4.3: Recurrent Neural Networks
  • Figure 5.4: U.S. Treasuries: Average Excess Return (%) by tenor for KF, EKF, PF 1-day-ahead predictions
  • Figure 5.5: Training result of U.S. Treasuries: Model loss
  • ...and 12 more figures

Theorems & Definitions (2)

  • Theorem 2.1
  • Proposition 2.2