How Arbitrage-Free is the Nelson-Siegel Model?
60 Pages Posted: 27 Feb 2008
Date Written: February 2008
We test whether the Nelson and Siegel (1987) yield curve model is arbitrage-free in a statistical sense. Theoretically, the Nelson-Siegel model does not ensure the absence of arbitrage opportunities, as shown by Bjork and Christensen (1999). Still, central banks and public wealth managers rely heavily on it. Using a non-parametric resampling technique and 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 NS model, at a 95 percent confidence level. We therefore conclude that the Nelson and Siegel yield curve model is compatible with arbitrage-freeness. To corroborate this result, we show that the Nelson-Siegel model performs as well as its no-arbitrage counterpart in an out-of-sample forecasting experiment.
Keywords: Nelson-Siegel model, No-arbitrage restrictions, affine term structure models, non-parametric test
JEL Classification: C14, C15, G12
Suggested Citation: Suggested Citation