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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.

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

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    1. Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," The 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, University of Reading.
    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. Bulíř, Aleš & Vlček, Jan, 2021. "Monetary transmission: Are emerging market and low-income countries different?," Journal of Policy Modeling, Elsevier, vol. 43(1), pages 95-108.
    2. Atkins, Philip J. & Cummins, Mark, 2023. "Improved scalability and risk factor proxying with a two-step principal component analysis for multi-curve modelling," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1331-1348.
    3. 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.
    4. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, August.
    5. 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.
    6. Martin Keller-Ressel, 2019. "The classification of term structure shapes in the two-factor Vasicek model -- a total positivity approach," Papers 1908.04667, arXiv.org, revised Jun 2021.
    7. Jaka Gogala & Joanne E. Kennedy, 2017. "CLASSIFICATION OF TWO- AND THREE-FACTOR TIME-HOMOGENEOUS SEPARABLE LMMs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-44, March.
    8. 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.

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    More about this item

    Keywords

    Principal components analysis; correlation matrix; term structure; total positivity; oscillation matrix; Schoenmakers-Coffey matrix;
    All these keywords.

    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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