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Interpolation Methods for Curve Construction

  • Patrick Hagan
  • Graeme West
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    This paper surveys a wide selection of the interpolation algorithms that are in use in financial markets for construction of curves such as forward curves, basis curves, and most importantly, yield curves. In the case of yield curves the issue of bootstrapping is reviewed and how the interpolation algorithm should be intimately connected to the bootstrap itself is discussed. The criterion for inclusion in this survey is that the method has been implemented by a software vendor (or indeed an inhouse developer) as a viable option for yield curve interpolation. As will be seen, many of these methods suffer from problems: they posit unreasonable expections, or are not even necessarily arbitrage free. Moreover, many methods lead one to derive hedging strategies that are not intuitively reasonable. In the last sections, two new interpolation methods (the monotone convex method and the minimal method) are introduced, which it is believed overcome many of the problems highlighted with the other methods discussed in the earlier sections.

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    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 13 (2006)
    Issue (Month): 2 ()
    Pages: 89-129

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    Handle: RePEc:taf:apmtfi:v:13:y:2006:i:2:p:89-129
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    1. Bing-Huei Lin, 2002. "Fitting term structure of interest rates using B-splines: the case of Taiwanese Government bonds," Applied Financial Economics, Taylor & Francis Journals, vol. 12(1), pages 57-75.
    2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
    3. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(04), pages 419-440, December.
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