A Modified Arbitrage-Free Nelson–Siegel Model: An Alternative Affine Term Structure Model of Interest Rates

Abstract

This paper derives a modified version of the Arbitrage-Free Nelson–Siegel (AFNS) model in which the Gaussian level factor in the AFNS model is replaced by a CIR process. By doing so, the resulting model is a subclass of the $$\mathbb {A}_1 (3)$$ class of affine dynamic term structure models, that tries to maintain the Nelson–Siegel (NS) property. Empirically, we found that for the US treasury data, our model fits better than AFNS, but that is offset by weaker forecasting performance for the very long maturities. For the Japanese Government Bond (JGB) zero-yields data, we found that there is no significant difference between our model and the AFNS model. In addition, for both data sets, our model to some extent, did maintain the NS property. We argued that because of the similarity between our model and the existing AFNS model, for modeling purpose it may be used as an alternative model. To our knowledge, this paper is the first to study the empirical performances and properties of the AFNS model for JGB zero-coupon yields.