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Statistical Properties of Forward Libor Rates

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  • Carol Alexander

    ()
    (ICMA Centre, University of Reading)

  • Dimitri Lvov

    ()
    (ICMA Centre, University of Reading)

Abstract

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.

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Bibliographic Info

Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2003-03.

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Length: 33 pages
Date of creation: Jan 2003
Date of revision:
Handle: RePEc:rdg:icmadp:icma-dp2003-03

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Related research

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

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References

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  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 409-30, 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. 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.
  3. Roger Lord & Antoon Pelsser, 2005. "Level-Slope-Curvature - Fact or Artefact?," Tinbergen Institute Discussion Papers 05-083/2, Tinbergen Institute.

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