Pricing the Term Structure of Interest Rates Using Linear Regressions

This white paper presents a methodology for estimating and analyzing the term structure of interest rates through a regression-based framework. The approach, based on the work of Adrian, Crump, and Moench (2013), allows for the estimation of affine term structure models without the need for numerical optimization. Instead, it utilizes a series of linear regressions, making it computationally feasible even with high-dimensional yield data and multiple pricing factors. The methodology is implemented in MATLAB, processing historical yield data, performing principal component analysis, estimating factor dynamics, and decomposing observed yields into expectations and term premia. The paper illustrates the practical application of this model using U.S. Treasury yields and U.K. government bond data, demonstrating its flexibility and robustness. The document also discusses the theoretical framework of the ACM model, the three-step estimation procedure, and the statistical inference and model diagnostics, providing insights into the accuracy and reliability of the methodology.