Pricing the Bund term structure with linear regressions – without an observable short rate - Christian Speck (Deutsche Bundesbank, 2023)
Affine term structure models of bond yields are important tools for analyzing fixed income markets and monetary policy. Estimators of Adrian, Crump, and Mönch (2013) and Diez de Los Rios (2015) replace time-consuming nonlinear search procedures with a set of simple linear regressions. However, these estimators require an observable short rate, which is not available at a one-month maturity for many markets, including that for German Bunds. This paper introduces new regression-based Difference Estimators that require no observable short rate but are determined from long-term yields only. My new estimators replicate results of the traditional estimators for US Treasuries, although my approaches omit the available US short rate. For German Bund data since 1967, three factors are sufficient to represent the yield curve dynamics, and additional restrictions improve yield forecasts. Implicit short Bund rates are in line with policy interest rates. The term premium is counter-cyclical to business activity and positively related to uncertainty. Thus, the Bund yield decomposition into short-rate expectations and the term premium is suitable for a wide range of policy applications.
Keywords: C13; E43; G12; 330; Yield Curve; Affine Term Structure Model; Bund Term Premium