A FAMILY OF MODELS EXPLAINING THE LEVEL-SLOPE-CURVATURE EFFECT

Liliana Forzani () and Carlos Tolmasky ()
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Liliana Forzani: School of Mathematics, University of Minnesota, 206 Chuch Street, Minneapolis, MN 55455, USA
Carlos Tolmasky: Cargill Inc. and School of Mathematics, 12700 Whitewater Drive, Minnetonka, MN 55343, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2003, vol. 06, issue 03, 239-255

Abstract: One of the most widely used methods to build yield curve models is to use principal components analysis on the correlation matrix of the innovations. R. Litterman and J. Scheinkman found that three factors are enough to explain most of the moves in the case of the US treasury curve. These factors are level, steepness and curvature. Working in the context of commodity futures, G. Cortazar and E. Schwartz found that the spectral structure of the correlation matrices is strikingly similar to those found by R. Litterman and J. Scheinkman. We observe that in both cases the correlation between two different contracts maturing at timestandsis roughly of the formρ|t-s|, for a certain (fixed)0 ≤ ρ ≤ 1. Assuming this correlation structure we prove that the observed factors are perturbations of cosine waves and we extend the analysis to multiple curves.

Keywords: Principal components analysis; Heath–Jarrow–Morton (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S021902490300192X

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