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A Family Of Models Explaining The Level-Slope-Curvature Effect

Author

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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)

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.

Suggested Citation

  • Liliana Forzani & Carlos Tolmasky, 2003. "A Family Of Models Explaining The Level-Slope-Curvature Effect," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 239-255.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:03:n:s021902490300192x
    DOI: 10.1142/S021902490300192X
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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. 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.
    3. 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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