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Statistical Properties of Forward Libor Rates


  • Carol Alexander

    () (ICMA Centre, University of Reading)

  • Dimitri Lvov

    () (ICMA Centre, University of Reading)


historical forward rates are used to calibrate the lognormal forward rate model - as advocated by Hull and White (1999, 2000), Longstaff, Santa Clara and Schwartz (1999), Rebonato (1999a,b,c), Rebonato and Joshi (2001) and many others - a Libor yield curve needs to be fit to the available data on spot libor rates, forward rate agreements (FRAs) or futures, and swap rates. This paper compares the statistical properties of the time series of forward rates that are obtained using three different yield curve fitting techniques. Introduced by McCulloch (1975), Steely (1991) and Svensson (1994), each of the three techniques is well known for its application to the construction of bond yield curves. Our work focuses on the eigenstructure of estimated forward rate correlation matrices. These are shown to be dominated by the semi-parametric or parametric form that is used in the yield curve model. The spectral decomposition of forward rate correlation - and covariance - matrices is considered in some detail, and in particular we test the common principal component hypothesis of Flury (1988), which has been applied to the lognormal forward rate model by Alexander (2003). We conclude that, if historical data are used to calibrate the lognormal forward rate model, it is best to use Svensson forward rate correlation matrices. However, the empirical evidence is strongly in favour of the common principal component hypothesis, where the three principal eigenvectors in all correlation matrices of the same dimension are identical. Hence we further conclude that a parsimonious parameterisation of forward rate correlations is possible, and this allows for direct calibration of forward rate correlations to market data, so historical data are not necessary.

Suggested Citation

  • Carol Alexander & Dimitri Lvov, 2003. "Statistical Properties of Forward Libor Rates," ICMA Centre Discussion Papers in Finance icma-dp2003-03, Henley Business School, Reading University.
  • Handle: RePEc:rdg:icmadp:icma-dp2003-03

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    References listed on IDEAS

    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
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    Cited by:

    1. Roger Lord & Antoon Pelsser, 2007. "Level-Slope-Curvature - Fact or Artefact?," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 105-130.
    2. Laurini, Márcio Poletti & Ohashi, Alberto, 2015. "A noisy principal component analysis for forward rate curves," European Journal of Operational Research, Elsevier, vol. 246(1), pages 140-153.
    3. Carol Alexandra, 2002. "Common Correlation and Calibrating the Lognormal Forward Rate Model," ICMA Centre Discussion Papers in Finance icma-dp2002-18, Henley Business School, Reading University, revised Jan 2003.

    More about this item


    Yield curve fitting; common principal component analysis; volatility; correlation; covariance; lognormal formal rate model;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling


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