Calibrating the Nelson-Siegel-Svensson Model

22 Pages Posted: 16 Sep 2010 Last revised: 22 Apr 2011

See all articles by Manfred Gilli

Manfred Gilli

University of Geneva - Research Center for Statistics; Swiss Finance Institute

Stefan Grosse

NORD/LB; University of Erfurt

Enrico Schumann


Date Written: March 30, 2010


The Nelson-Siegel-Svensson model is widely-used for modelling the yield curve, yet many authors have reported ‘numerical difficulties’ when calibrating the model. We argue that the problem is twofold: firstly, the optimisation problem is not convex and has multiple local optima. Hence standard methods that are readily available in statistical packages are not appropriate. We implement and test an optimisation heuristic, Differential Evolution, and show that it is capable of reliably solving the model. Secondly, we also stress that in certain ranges of the parameters, the model is badly conditioned, thus estimated parameters are unstable given small perturbations of the data. We discuss to what extent these difficulties affect applications of the model.

Keywords: Interest Rate Models, Term Structure Models, Nelson-Siegel, Nelson-Siegel-Svensson, Differential Evolution, R

JEL Classification: G12, G17, E43, E47, C51, C61, C63

Suggested Citation

Gilli, Manfred and Grosse, Stefan and Schumann, Enrico, Calibrating the Nelson-Siegel-Svensson Model (March 30, 2010). Available at SSRN: or

Manfred Gilli

University of Geneva - Research Center for Statistics ( email )

+41223798222 (Phone)
+41223798299 (Fax)


Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

Stefan Grosse

NORD/LB ( email )

Friedrichswall 10
Hannover, 30159
+49-511-3612365 (Phone)
+49-511-361982365 (Fax)

University of Erfurt ( email )

Internationales Buro
Nordhaeuser Str. 63
D - 99089 Erfurt

Enrico Schumann (Contact Author)

Independent ( email )

No Address Available

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