State-Space Dynamic Functional Regression for Multicurve Fixed Income Spread Analysis and Stress Testing

TL;DR

This paper introduces a novel state-space functional regression model combining the Nelson-Siegel framework with kernel PCA for fixed income spread analysis and stress testing across economies.

Contribution

It develops a dynamic, multi-economy functional regression model that improves yield spread explanation and calibration using kernel PCA, with empirical validation and stress testing.

Findings

The model effectively explains yield spreads between economies.

Kernel PCA facilitates tractable estimation of functional regression.

Empirical analysis shows improved in-sample performance over traditional models.

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.