A note on the long rate in factor models of the term structure

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.

Netspar, Network for Studies on Pensions, Aging and Retirement, is a thinktank and knowledge network. Netspar is dedicated to promoting a wider understanding of the economic and social implications of pensions, aging and retirement in the Netherlands and Europe.


Mission en strategy           •           Network           •           Organisation           •          Magazine
Board Brief            •            Actionplan 2023-2027           •           Researchagenda


Our partners

View all partners