A yield-macro model for actuarial use in the U.K

The aim of this study is to construct yield curve models for UK nominal interest rates, real interest rates and implied inflation rates considering the linkage between their term structures and some macroeconomic variables, in particular, realised inflation and output gap. We start with fitting a descriptive yield curve model proposed by Cairns (1998) to fill the missing values for some given days at some given maturities in the data provided by the Bank of England. Applying principal component analysis to the fitted values we find three principal components namely, level, slope and curvature for each yield curve. We explore the bi-directional relations between these principal components and the macroeconomic variables to construct a yield-macro model. Although simple autoregressive order one models are enough to model the level factors, slope and curvature factors can be modelled better inserting the realised inflation or output gap as explanatory variables. We also model macroeconomic variables that take the term structures into account.