A Note on the Long Rate in Factor Models of the Term Structure

10 Pages Posted: 2 Apr 2016  

Jan De Kort

University of Amsterdam

Multiple version iconThere are 2 versions of this paper

Date Written: March 10, 2016


We show that, as a consequence of the Dybvig-Ingersoll-Ross theorem, the existence of a non-deterministic long rate in a factor model of the term structure implies that the model has an equivalent representation in which one of the state variables is nondecreasing. Moreover, for two-dimensional factor models, we prove that if the long rate is non-deterministic, the yield curve flattens out and the factor process is asymptotically non-deterministic, then the term structure is unbounded. Finally, following up on an open question in El Karoui et al. (1997), we provide an explicit example of a three-dimensional affine factor model with a non-deterministic yet finite long rate in which volatility of the factor process does not vanish over time.

Keywords: Long rate, factor model, term structure, Dybvig-Ingersoll-Ross Theorem

Suggested Citation

De Kort, Jan, A Note on the Long Rate in Factor Models of the Term Structure (March 10, 2016). Netspar Discussion Paper No. 03/2016-014. Available at SSRN: https://ssrn.com/abstract=2757588 or http://dx.doi.org/10.2139/ssrn.2757588

Jan De Kort (Contact Author)

University of Amsterdam ( email )

Spui 21
Amsterdam, 1018 WB

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