A Note on the Nelson–Siegel Family
Article first published online: 25 DEC 2001
Blackwell Publishers Inc 1999
Volume 9, Issue 4, pages 349–359, October 1999
How to Cite
Filipović, D. (1999), A Note on the Nelson–Siegel Family. Mathematical Finance, 9: 349–359. doi: 10.1111/1467-9965.00073
- Issue published online: 21 APR 2004
- Article first published online: 25 DEC 2001
- Cited By
- interest rate model;
- Nelson–Siegel family;
- consistent state space Itô process;
- inverse problem.
We study a problem posed in Bj"ork 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 Itô 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 Itô process.