How arbitrage-free is the Nelson-Siegel Model? - Laura Coroneo; Ken Nyholm; Rositsa Vidova-Koleva (European Central Bank (ECB), 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 fore-casting experiment.
Keywords: C14; C15; G12; 330; Affine term structure models; Nelson-Siegel model; No-arbitrage restrictions; non-parametric test; Zinsstruktur; Arbitrage Pricing; Kapitaleinkommen; Mathematische Optimierung; Theorie