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Term structure extrapolation and asymptotic forward rates

Author

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  • de Kort, J.
  • Vellekoop, M.H.
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.

Suggested Citation

  • de Kort, J. & Vellekoop, M.H., 2016. "Term structure extrapolation and asymptotic forward rates," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 107-119.
    • Handle: RePEc:eee:insuma:v:67:y:2016:i:c:p:107-119
    DOI: 10.1016/j.insmatheco.2015.11.001
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    References listed on IDEAS

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    Cited by:

    1. Lagerås, Andreas & Lindholm, Mathias, 2016. "Issues with the Smith–Wilson method," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 93-102.
    2. Florian Gach, 2016. "Note On The Smith–Wilson Interest Rate Curve," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-16, November.
    3. Balter, Anne G. & Pelsser, Antoon & Schotman, Peter C., 2021. "What does a term structure model imply about very long-term interest rates?," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 202-219.
    4. Jørgensen, Peter Løchte, 2018. "An analysis of the Solvency II regulatory framework’s Smith-Wilson model for the term structure of risk-free interest rates," Journal of Banking & Finance, Elsevier, vol. 97(C), pages 219-237.
    5. Lutz Kruschwitz, 2018. "Das Problem der Anschlussverzinsung," Schmalenbach Journal of Business Research, Springer, vol. 70(1), pages 9-45, March.
    6. Zhao, Chaoyi & Jia, Zijian & Wu, Lan, 2024. "Construct Smith-Wilson risk-free interest rate curves with endogenous and positive ultimate forward rates," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 156-175.

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