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Interpolation Methods for Curve Construction

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  • Patrick Hagan
  • Graeme West
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    Abstract

    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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    Bibliographic Info

    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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    Related research

    Keywords: Yield curve; interpolation; bootstrap;

    References

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    1. 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.
    2. 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.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
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    Cited by:
    1. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2010. "Collateral Posting and Choice of Collateral Currency - Implications for Derivative Pricing and Risk Management-," CIRJE F-Series CIRJE-F-743, CIRJE, Faculty of Economics, University of Tokyo.
    2. Bianchetti, Marco, 2008. "Two Curves, One Price :Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves," MPRA Paper 22022, University Library of Munich, Germany, revised 24 Jan 2010.
    3. Jan-Frederik Mai & Marc Wittlinger, 2013. "Pricing bonds with optional sinking feature using Markov Decision Processes," Papers 1305.5220, arXiv.org.
    4. Masaaki Fujii & Akihiko Takahashi, 2010. "Modeling of Interest Rate Term Structures under Collateralization and its Implications," CIRJE F-Series CIRJE-F-762, CIRJE, Faculty of Economics, University of Tokyo.
    5. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CARF F-Series CARF-F-196, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Apr 2011.
    6. Lim, Kyuseong & Kim, Min Jae & Kim, Sehyun & Kim, Soo Yong, 2014. "Statistical properties of the stock and credit market: RMT and network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 66-75.
    7. Erdemlioglu, Deniz, 2009. "Macro Factors in UK Excess Bond Returns: Principal Components and Factor-Model Approach," MPRA Paper 28895, University Library of Munich, Germany.
    8. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CIRJE F-Series CIRJE-F-698, CIRJE, Faculty of Economics, University of Tokyo.
    9. Borak, Szymon & Weron, Rafal, 2008. "A semiparametric factor model for electricity forward curve dynamics," MPRA Paper 10421, University Library of Munich, Germany.
    10. Paul Beaumont & Yaniv Jerassy-Etzion, 2011. "Computing maximally smooth forward rate curves for coupon bonds: An iterative piecewise quartic polynomial interpolation method," Working Papers wp2011_08_03, Department of Economics, Florida State University.
    11. Areski Cousin & Ibrahima Niang, 2014. "On the range of admissible term-structures," Papers 1404.0340, arXiv.org.
    12. Masaaki Fujii & Akihiko Takahashi, 2010. "Modeling of Interest Rate Term Structures under Collateralization and its Implications," CARF F-Series CARF-F-230, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Dec 2010.
    13. Mark H. A. Davis & Vicente Mataix-Pastor, 2009. "Arbitrage-Free Interpolation Of The Swap Curve," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 969-1005.
    14. Tao Peng, 2010. "Portfolio Credit Risk Modelling and CDO Pricing - Analytics and Implied Trees from CDO Tranches," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 8.
    15. Areski Cousin & Ibrahima Niang, 2014. "On the Range of Admissible Term-Structures," Working Papers hal-00968943, HAL.

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