Working Paper presents research work by both Danmarks Nationalbank’s employees and our partners. The series is primarily targeted at professionals and people with an interest in central banking research as well as economics and finance in a broader sense.

Working paper: Modelling Danish Government Bond Yields in a Low-Rate Environment

We model the dynamics of Danish government bond yields in a low-rate environment using a shadow-rate term structure model, which imposes a lower bound on the yields. In contrast to findings in the literature for other countries, we do not observe notable improvements when applying a shadow-rate model to the Danish case, as the model is challenged by the declining trend of the Danish rates into negative territory.

​We model the dynamics of Danish government bond yields in a low-rate environment using a term structure model with a lower bound, a so-called shadow rate model. Specifically, we use a shadow rate extension of the well-known Arbitrage-Free Nelson--Siegel model. In the literature, shadow rate models have been shown to improve the cross-sectional fit and the forecast performance when interest rates are close to zero. We do not, however, identify such improvements when using a shadow rate model on Danish yield data. The reason is that the shadow rate model is challenged when rates continue to decline into negative territory as has been the case in Denmark in recent years. Despite the challenges, we still prefer a shadow rate model over Gaussian models as the former captures the asymmetric distribution of future rates that characterises the low-yield environment. From a risk management perspective, we find that the shadow rate extension influences the term premia estimates notably only for a brief period in the beginning of 2015, where rates were at their lowest. Finally, as an aside we find that a term structure model with two rather than three factors improves the forecast performance in the low-rate period.