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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.

Suggested Citation

  • Roger Lord & Antoon Pelsser, 2007. "Level-Slope-Curvature - Fact or Artefact?," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 105-130.
  • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:105-130 DOI: 10.1080/13504860600661111

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    References listed on IDEAS

    1. 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 149-185.
    2. Lars E.O. Svensson, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994," NBER Working Papers 4871, National Bureau of Economic Research, Inc.
    3. 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, August.
    4. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
    5. 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.
    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 473-489, October.
    7. 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.
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    Cited by:

    1. Laurini, Márcio Poletti & Ohashi, Alberto, 2015. "A noisy principal component analysis for forward rate curves," European Journal of Operational Research, Elsevier, vol. 246(1), pages 140-153.
    2. Ales Bulir & Jan Vlcek, 2015. "Monetary Transmission; Are Emerging Market and Low Income Countries Different?," IMF Working Papers 15/239, International Monetary Fund.
    3. Iliya Markov & Rodrigue Oeuvray & Nils Tuchschmid, 2013. "Non-fully invested derivative-free bond index replication," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(1), pages 101-124, March.
    4. repec:wsi:ijtafx:v:20:y:2017:i:02:n:s0219024917500212 is not listed on IDEAS
    5. Polychronis Manousopoulos & Michalis Michalopoulos, 2015. "Term structure of interest rates estimation using rational Chebyshev functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(2), pages 119-146, October.

    More about this item


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

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)


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