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Level-Slope-Curvature - Fact or Artefact?

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  • Roger Lord
  • Antoon Pelsser

Abstract

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 generalizations 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 a conjecture that the order present in correlation matrices cause slope.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 14 (2007)
Issue (Month): 2 ()
Pages: 105-130

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Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:105-130

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Keywords: Principal components analysis; correlation matrix; term structure; total positivity; oscillation matrix; Schoenmakers-Coffey matrix;

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  1. Jong, F.C.J.M. de & Driessen, J. & Pelsser, A., 2004. "On the information in the interest rate term structure and option prices," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3159390, Tilburg University.
  2. Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 149-85.
  3. Carol Alexander & Dimitri Lvov, 2003. "Statistical Properties of Forward Libor Rates," ICMA Centre Discussion Papers in Finance icma-dp2003-03, Henley Business School, Reading University.
  4. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October.
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