Term structure extrapolation and asymptotic forward rates

Jan de Kort, M.H. Vellekoop

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We investigate different inter- and extrapolation methods for term structures under different constraints in order to generate market-consistent estimates which describe the asymptotic behavior of forward rates. Our starting point is the method proposed by Smith and Wilson, which is used by the European insurance supervisor EIOPA. We use the characterization of the Smith–Wilson class of interpolating functions as the solution to a functional optimization problem to extend their approach in such a way that forward rates will converge to a value which is an outcome of the optimization process. Precise conditions are stated which guarantee that the optimization problems involved are well-posed on appropriately chosen function spaces. As a result, a well-defined optimal asymptotic forward rate can be derived directly from prices and cashflows of traded instruments. This allows practitioners to use raw market data to extract information about long term forward rates, as we will show in a study which analyzes historical EURIBOR swap data.
Original languageEnglish
Pages (from-to)107-119
JournalInsurance: Mathematics and Economics
Volume67
DOIs
Publication statusPublished - 2016
Externally publishedYes

Fingerprint

Term Structure
Extrapolation
Optimization Problem
Extrapolation Method
Consistent Estimates
Swap
Interpolation Method
Process Optimization
Insurance
Function Space
Well-defined
Asymptotic Behavior
Converge
Term
Market
Forward rates
Term structure
Class
Optimization problem

Keywords

  • term structure
  • extrapolation
  • asymptotic forward rates
  • Smith-Wilson algorithm
  • exponential tension spline

Cite this

de Kort, Jan ; Vellekoop, M.H. / Term structure extrapolation and asymptotic forward rates. In: Insurance: Mathematics and Economics. 2016 ; Vol. 67. pp. 107-119.
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Term structure extrapolation and asymptotic forward rates. / de Kort, Jan; Vellekoop, M.H.

In: Insurance: Mathematics and Economics, Vol. 67, 2016, p. 107-119.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Vellekoop, M.H.

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AB - We investigate different inter- and extrapolation methods for term structures under different constraints in order to generate market-consistent estimates which describe the asymptotic behavior of forward rates. Our starting point is the method proposed by Smith and Wilson, which is used by the European insurance supervisor EIOPA. We use the characterization of the Smith–Wilson class of interpolating functions as the solution to a functional optimization problem to extend their approach in such a way that forward rates will converge to a value which is an outcome of the optimization process. Precise conditions are stated which guarantee that the optimization problems involved are well-posed on appropriately chosen function spaces. As a result, a well-defined optimal asymptotic forward rate can be derived directly from prices and cashflows of traded instruments. This allows practitioners to use raw market data to extract information about long term forward rates, as we will show in a study which analyzes historical EURIBOR swap data.

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