Paper: arXiv 2409.00348

Abstract

The Nelson-Siegel model is widely used in fixed income markets to produce yield curve dynamics. The multiple time-dependent parameter model conveniently addresses the level, slope, and curvature dynamics of the yield curves. In this study, we present a novel state-space functional regression model that incorporates a dynamic Nelson-Siegel model and functional regression formulations applied to multi-economy setting. This framework offers distinct advantages in explaining the relative spreads in yields between a reference economy and a response economy. To address the inherent challenges of model calibration, a kernel principal component analysis is employed to transform the representation of functional regression into a finite-dimensional, tractable estimation problem. A comprehensive empirical analysis is conducted to assess the efficacy of the functional regression approach, including an in-sample performance comparison with the dynamic Nelson-Siegel model. We conducted the stress testing analysis of yield curves term-structure within a dual economy framework. The bond ladder portfolio was examined through a case study focused on spread modelling using historical data for US Treasury and UK bonds.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical techniques including state-space models, functional regression, and kernel PCA, requiring dense theory and derivations. It also demonstrates strong empirical application with comprehensive historical data analysis, performance comparisons, stress testing, and a practical bond ladder case study, alongside accessible code and data availability.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Model Yield Curve Spreads &<br>Stress Test Multi-Economy Bonds"] --> B{"Data Inputs"};
  B --> C["US & UK Treasury Data"];
  B --> D["Nelson-Siegel<br>Parameters"];
  
  C --> E["State-Space Functional Regression<br>with Kernel PCA"];
  D --> E;
  
  E --> F{"Model Assessment"};
  F --> G["In-Sample Performance<br>vs. Dynamic Nelson-Siegel"];
  F --> H["Stress Testing<br>Dual Economy Framework"];
  
  G --> I["Key Outcomes"];
  H --> I;
  
  I --> J["Effective Spread Modeling<br>via Functional Regression"];
  I --> K["Robust Stress Testing<br>on Bond Ladder Portfolios"];