Level-Slope-Curvature - Fact or Artefact?
Applied Mathematical Finance, Vol. 14, No. 2, 2007
Tinbergen Institute Discussion Paper No. TI 05-083/2
32 Pages Posted: 20 Sep 2005 Last revised: 9 May 2011
Date Written: September 1, 2005
The first three factors resulting from a principal components analysis of term structure data are in the literature typically interpreted as driving the level, slope and curvature of the term structure. Using slight generalisations of theorems from total positivity, we present sufficient conditions under which level, slope and curvature are present. These conditions have the nice interpretation of restricting the level, slope and curvature of the correlation surface. It is proven that the Schoenmakers-Coffey correlation matrix also brings along such factors. Finally, we formulate and corroborate our conjecture that the order present in correlation matrices causes slope.
Keywords: Principal components analysis, correlation matrix, total positivity, oscillation matrix, Schoenmakers-Coffey matrix
JEL Classification: C50, C60, G10
Suggested Citation: Suggested Citation