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

Peilun He, Gareth W. Peters, Nino Kordzakhiac, Pavel V. Shevchenko
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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.
用于多曲线固定收益利差分析和压力测试的状态空间动态函数回归
Nelson-Siegel 模型被广泛应用于固定收益市场的收益率曲线动态分析。这种多时间参数模型可以方便地处理收益率曲线的水平、斜率和曲率动态。在本研究中,我们提出了一个新颖的状态空间函数回归模型,该模型将动态 Nelson-Siegel 模型和函数回归公式结合起来,应用于多经济体环境。这一框架在解释参照经济体和响应经济体之间收益率的相对利差方面具有明显的优势。为了解决模型校准的固有难题,我们采用了核主成分分析法,将函数回归的表述转化为有限维度的可控估计问题。我们进行了全面的实证分析,以评估函数回归方法的有效性,包括与动态 Nelson-Siegel 模型的样本内性能比较。我们在二元经济框架内对收益率曲线的期限结构进行了压力测试分析。我们利用美国国债和英国债券的历史数据,通过以利差建模为重点的案例研究,对债券阶梯组合进行了检验。
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