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Modelling the Yield Curve with Orthonormalised Laguerre Polynomials: A Consistent Cross-Sectional and Inter-Temporal Approach

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  • Leo Krippner

    () (AMP Capital Investors)

Abstract

This article proposes the orthonormalised Laguerre polynomial (OLP) model of the yield curve, a generic linear model that is both cross-sectionally consistent (that is, it reliably fits the yield curve at a given point in time), and inter-temporally consistent (that is, the cross-sectional parameters are shown to be consistent over time within the expectations hypothesis framework). The OLP model generalises the exponential-polynomial model for a single yield curve, as originally proposed by Nelson and Siegel (1987), and also allows for the simultaneous modelling of other same-currency yield curves that have instrument-specific differences (such as default risk), as in Houweling, Hoek and Kleibergen (2001). New Zealand data is used to illustrate the empirical application of the OLP model.

Suggested Citation

  • Leo Krippner, 2003. "Modelling the Yield Curve with Orthonormalised Laguerre Polynomials: A Consistent Cross-Sectional and Inter-Temporal Approach," Working Papers in Economics 03/02, University of Waikato.
  • Handle: RePEc:wai:econwp:03/02
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    File URL: ftp://wms-webprod1.mngt.waikato.ac.nz/RePEc/wai/econwp/0302.pdf
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    References listed on IDEAS

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    1. Jean Helwege & Christopher M. Turner, 1999. "The Slope of the Credit Yield Curve for Speculative-Grade Issuers," Journal of Finance, American Finance Association, vol. 54(5), pages 1869-1884, October.
    2. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October.
    3. 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.
    4. Houweling, Patrick & Hoek, Jaap & Kleibergen, Frank, 2001. "The joint estimation of term structures and credit spreads," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 297-323, July.
    5. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453 World Scientific Publishing Co. Pte. Ltd..
    6. Ben Hunt, 1995. "Fitting Parsimonious Yield Curve Models to Australian Coupon Bond Data," Working Paper Series 51, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Pham, Toan M., 1998. "Estimation of the term structure of interest rates: an international perspective," Journal of Multinational Financial Management, Elsevier, vol. 8(2-3), pages 265-283, September.
    8. Hördahl, Peter, 2000. "Estimating the implied distribution of the future short term interest rate using the Longstaff-Schwartz model," Working Paper Series 0016, European Central Bank.
    9. 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.
    10. Seppälä, Juha & Viertiö, Petri, 1996. "The term structure of interest rates : Estimation and interpretation," Research Discussion Papers 19/1996, Bank of Finland.
    11. Schich, Sebastian T., 1997. "Estimating the German term structure," Discussion Paper Series 1: Economic Studies 1997,04e, Deutsche Bundesbank.
    12. Mansi, Sattar A & Phillips, Jeffrey H, 2001. "Modeling the Term Structure from the On-the-Run Treasury Yield Curve," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 545-564, Winter.
    13. 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. Leo Krippner, 2005. "An Intertemporally-Consistent and Arbitrage-Free Version of the Nelson and Siegel Class of Yield Curve Models," Working Papers in Economics 05/01, University of Waikato.
    2. Leo Krippner, 2003. "Modelling the Yield Curve with Orthonomalised Laguerre Polynomials: An Intertemporally Consistent Approach with an Economic Interpretation," Working Papers in Economics 03/01, University of Waikato.

    More about this item

    Keywords

    yield curve; term structure; expectations hypothesis; exponential polynomial; Nelson and Siegel model;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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