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

See all articles by Roger Lord

Roger Lord

Cardano Risk Management

Antoon Pelsser

Maastricht University; Netspar

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

Lord, Roger and Pelsser, Antoon A. J., Level-Slope-Curvature - Fact or Artefact? (September 1, 2005). Applied Mathematical Finance, Vol. 14, No. 2, 2007, Tinbergen Institute Discussion Paper No. TI 05-083/2, Available at SSRN: https://ssrn.com/abstract=802465

Roger Lord (Contact Author)

Cardano Risk Management ( email )

Rotterdam 3011 AA

Antoon A. J. Pelsser

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE

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