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

Jan de Kort

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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 language English 656-667 Mathematical Finance 28 2 https://doi.org/10.1111/mafi.12151 Published - Apr 2018

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Term Structure
Factor Models
Flatten
Volatility
Filtration
Vanish
Imply
Three-dimensional
Curve
Term structure
Theorem
Factors

Keywords

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

Cite this

de Kort, Jan. / A note on the long rate in factor models of the term structure. In: Mathematical Finance. 2018 ; Vol. 28, No. 2. pp. 656-667.
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In: Mathematical Finance, Vol. 28, No. 2, 04.2018, p. 656-667.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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 theDybvig–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.

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