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Updating the Ultimate Forward Rate over Time: A Possible Approach

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  • Diana Zigraiova
  • Petr Jakubik

Abstract

This study proposes a potential methodological approach to be used by regulators when updating the Ultimate Forward Rate (UFR) for the evaluation of insurers' liabilities beyond the last liquid point observable in the market. Our approach is based on the optimisation of two contradictory aspects - stability and accuracy implied by economic fundamentals. We use U.S. Treasury term structure data over the period 1985-2015 to calibrate an algorithm that dynamically revises the UFR based on the distance between the value implied by the long-term growth of economic fundamentals in a given year and the regulatory value of the UFR valid in the prior year. We employ both the Nelson-Siegel and Svensson models to extrapolate yields over maturities of 21-30 years employing the selected value of the UFR and compare them with the observed yields using the mean square error statistic. Furthermore, we optimise the parameters of the proposed UFR formula by minimising the defined loss function capturing both mentioned factors.

Suggested Citation

  • Diana Zigraiova & Petr Jakubik, 2017. "Updating the Ultimate Forward Rate over Time: A Possible Approach," Working Papers 2017/03, Czech National Bank.
  • Handle: RePEc:cnb:wpaper:2017/03
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    References listed on IDEAS

    as
    1. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    2. Lars E.O. Svensson, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994," NBER Working Papers 4871, National Bureau of Economic Research, Inc.
    3. Oded Galor & Joseph Zeira, 1993. "Income Distribution and Macroeconomics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(1), pages 35-52.
    4. Casper Christophersen & Petr Jakubik, 2014. "Insurance and the Macroeconomic Environment," EIOPA Financial Stability Report - Thematic Articles 1, EIOPA, Risks and Financial Stability Department.
    5. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    6. De Pooter, Michiel & Ravazzolo, Francesco & van Dijk, Dick, 2006. "Predicting the term structure of interest rates incorporating parameter uncertainty, model uncertainty and macroeconomic information," MPRA Paper 2512, University Library of Munich, Germany, revised 03 Mar 2007.
    7. Hanson, Samuel G. & Stein, Jeremy C., 2015. "Monetary policy and long-term real rates," Journal of Financial Economics, Elsevier, vol. 115(3), pages 429-448.
    8. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
    9. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230, National Bureau of Economic Research, Inc.
    10. Duffee, Gregory R, 1996. "Idiosyncratic Variation of Treasury Bill Yields," Journal of Finance, American Finance Association, vol. 51(2), pages 527-551, June.
    11. James H. Stock & Mark W. Watson, 2003. "Has the business cycle changed?," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 9-56.
    12. Macit, Fatih, 2012. "Who responds more to monetary policy, conventional banks or participation banks?," Journal of Economics, Finance and Administrative Science, Universidad ESAN, vol. 17(33), pages 10-14.
    13. Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2011. "How arbitrage-free is the Nelson-Siegel model?," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 393-407, June.
    14. 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.
    15. Thomas Laubach & John C. Williams, 2003. "Measuring the Natural Rate of Interest," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1063-1070, November.
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    More about this item

    Keywords

    Extrapolation; Nelson-Siegel; Svensson; term structure of interest rates; Ultimate Forward Rate;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • L51 - Industrial Organization - - Regulation and Industrial Policy - - - Economics of Regulation
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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