Statistical Properties of Forward Libor Rates
Carol Alexander () and
Dimitri Lvov ()
Additional contact information
Dimitri Lvov: ICMA Centre, University of Reading
ICMA Centre Discussion Papers in Finance from Henley Business School, 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.Â 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.
Keywords: Yield curve fitting; common principal component analysis; volatility; correlation; covariance; lognormal formal rate model (search for similar items in EconPapers)
JEL-codes: C12 C14 C22 C5 G12 (search for similar items in EconPapers)
Pages: 33 pages
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5) Track citations by RSS feed
Downloads: (external link)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://www.icmacentre.ac.uk/pdf/discussion/DP2003-03.pdf [302 Found]--> https://www.icmacentre.ac.uk/pdf/discussion/DP2003-03.pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:rdg:icmadp:icma-dp2003-03
Access Statistics for this paper
More papers in ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading Contact information at EDIRC.
Bibliographic data for series maintained by Marie Pearson ().