A Note on the Nelson-Siegel Family

11 Pages Posted: 17 Jun 2004

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute


We study a problem posed in Bjork and Christensen (1999): Does there exist any nontrivial interest rate model that is consistent with the Nelson-Siegel family? They show that within the Heath-Jarrow-Morton framework with deterministic volatility structure the answer is no.

In this paper, we give a generalized version of this result including stochastic volatility structure. For that purpose, we introduce the class of consistent state space processes, which have the property to provide an arbitrage-free interest rate model when representing the parameters of the Nelson-Siegel family. We characterize the consistent state space Ito processes in terms of their drift and diffusion coefficients. By solving an inverse problem, we find their explicit form. It turns out that there exists no nontrivial interest rate model driven by a consistent state space Ito process.

Keywords: Interest rate model, Nelson-Siegel family, consistent state space Ito process, inverse problem

Suggested Citation

Filipovic, Damir, A Note on the Nelson-Siegel Family. Mathematical Finance, Vol. 9, pp. 349-359, October 1999. Available at SSRN: https://ssrn.com/abstract=534153

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Station 5
Lausanne, 1015

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

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

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