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A General Framework for the Construction and the Smoothing of Forward Rate Curves

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  • Oh-Kang Kwon

Abstract

This paper establishes a general theoretical and numerical framework for the construction and the smoothing of instantaneous forward rate curves. It is shown that if the smoothness of a curve is defined as an integral of a function in the derivatives of the curve, then the optimal curves are splines that satisfy certain ordinary differential equations. For such curves, and efficient numerical method is given for the determination of the spline parameters subject to mild assumptions. The resulting forward rate curves do not generally possess the desired degree of smoothness due mainly to the constraints imposed on the curves by the various market observed prices. A Partial solution to this problem is then introduced which achieves additional smoothing by taking into account the bid-ask ranges of each market rate. This eliminates much of the oscillatory patterns and the points of high curvature, and produces curves that are ideal for applications such as the estimation of interest rate models, and the pricing and risk management of interest rate derivatives, which are sensitive to forward rate curves.

Suggested Citation

  • Oh-Kang Kwon, 2002. "A General Framework for the Construction and the Smoothing of Forward Rate Curves," Research Paper Series 73, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:73
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp73.pdf
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    1. Chambers, Donald R. & Carleton, Willard T. & Waldman, Donald W., 1984. "A New Approach to Estimation of the Term Structure of Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(3), pages 233-252, September.
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    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Lars E.O. Svensson, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994," NBER Working Papers 4871, National Bureau of Economic Research, Inc.
    5. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
    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.
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    Cited by:

    1. Bystrom, Hans & Kwon, Oh Kang, 2007. "A simple continuous measure of credit risk," International Review of Financial Analysis, Elsevier, vol. 16(5), pages 508-523.
    2. Julian Manzano & Jorgen Blomvall, 2004. "Positive forward rates in the maximum smoothness framework," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 221-232.
    3. Damir Filipović & Sander Willems, 2016. "Exact Smooth Term Structure Estimation," Swiss Finance Institute Research Paper Series 16-38, Swiss Finance Institute.

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