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

Research output: Scientific - peer-reviewArticle

In this paper, we consider factor models of the term structure based on a Brownian filtration. We show that the existence of a nondeterministic long rate in a factor model of the term structure implies, as a consequence of the
Dybvig–Ingersoll–Ross theorem, that the model has an equivalent representation in which one of the state variables is nondecreasing. For two-dimensional factor models, we prove moreover that if the long rate is nondeterministic, the yield curve flattens out, and the factor process is
asymptotically nondeterministic, then the term structure is unbounded. Finally, we provide an explicit example of a three-dimensional affine factor model with a nondeterministic yet finite long rate in which the volatility of the factor
process does not vanish over time.
Original languageEnglish
Pages (from-to)1
Number of pages12
JournalMathematical Finance
StateE-pub ahead of print - 18 Apr 2017

    Research areas

  • Dybvig–Ingersoll–Ross theorem, factor model, long rate, term structure


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