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Term structure extrapolation and asymptotic forward rates

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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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    1. Leif Andersen, 2007. "Discount curve construction with tension splines," Review of Derivatives Research, Springer, vol. 10(3), pages 227-267, December.
    2. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. Barzanti, Luca & Corradi, Corrado, 1998. "A note on interest rate term structure estimation using tension splines," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 139-143, June.
    5. Svensson, L.E.O., 1994. "Estimating and Interpreting Foreward Interest Rates: Sweden 1992-1994," Papers 579, Stockholm - International Economic Studies.
    6. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    7. Cairns, A.J.G. & Pritchard, D.J., 2001. "Stability of Models for the Term Structure of Interest Rates with Application to German Market Data," British Actuarial Journal, Cambridge University Press, vol. 7(3), pages 467-507, August.
    8. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
    9. Mark Fisher & Douglas Nychka & David Zervos, 1995. "Fitting the term structure of interest rates with smoothing splines," Finance and Economics Discussion Series 95-1, Board of Governors of the Federal Reserve System (U.S.).
    10. Brian P. Sack, 2000. "Using Treasury STRIPS to measure the yield curve," Finance and Economics Discussion Series 2000-42, Board of Governors of the Federal Reserve System (U.S.).
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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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