A Generalized Arbitrage-Free Nelson-Siegel Term Structure Model with Macroeconomic Fundamentals

Abstract

This paper proposes a generalized arbitrage-free macro finance term structure model with both Nelson-Siegel latent yield factors and observable macro factors. Two subclasses are derived: spanned and unspanned models. In the spanned model, the yields are determined by both the Nelson-Siegel yield factors and macro variables. In the unspanned model, the yields are not spanned by macro variables but are only determined by the three Nelson-Siegel yield factors, although the Nelson-Siegel yield factors and macro variables interact in the state dynamics. Compared with existing models, the unspanned model is not only theoretically appealing but also proved to be empirically encouraging. We show that the new model improves predictive accuracy for long term yields than models with Nelson-Siegel yield factors only, with or without no-arbitrage restrictions; it can also improve forecast performance for nearly the whole yield curve than reduced-form dynamic Nelson-Siegel models, with or without macro factors. We also show the usefulness of this type of model in risk premia decomposition and explaining excess returns of yields.