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Level-Slope-Curvature - Fact or Artefact?

  • Roger Lord
  • Antoon Pelsser

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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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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  1. Svensson, L.E.O., 1994. "Estimating and Interpreting Foreward Interest Rates: Sweden 1992-1994," Papers 579, Stockholm - International Economic Studies.
  2. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
  3. Carlos Tolmasky & Dmitry Hindanov, 2002. "Principal components analysis for correlated curves and seasonal commodities: The case of the petroleum market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(11), pages 1019-1035, November.
  4. 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.
  5. Frank de Jong & Joost Driessen & Antoon Pelsser, 2004. "On the Information in the Interest Rate Term Structure and Option Prices," Review of Derivatives Research, Springer, vol. 7(2), pages 99-127, 08.
  6. 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.
  7. 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.
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