How arbitrage-free is the Nelson–Siegel model?

We test whether the Nelson and Siegel (1987) yield curve model is arbitrage-free. Theoretically, the Nelson–Siegel model does not ensure the absence of arbitrage opportunities, as shown by Bjork and Christensen (1999) and Filipovic (1999). Still, central banks and wealth managers rely heavily on it. Using zero-coupon yield curve data from the US market, we find that the no-arbitrage parameters are not statistically different from those obtained from the Nelson–Siegel model. We therefore conclude that the Nelson–Siegel yield curve model is compatible with the no-arbitrage constraints on the US market. To corroborate this result, we also show that the Nelson–Siegel model performs as well as its no-arbitrage counterpart in an out-of-sample forecasting experiment.