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Correlation Matrices of yields and Total Positivity

Author

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  • Ernesto Salinelli
  • Carlo Sgarra

    (SEMEQ Department - Faculty of Economics - University of Eastern Piedmont)

Abstract

It has been empirically observed that correlation matrices of forward interest rates have the first three eigenvalues which are simple and their corresponding eigenvectors, termed as shift, slope and curvature respectively, with elements presenting changes of sign in a regular way. These spectral properties are very similar to those exhibited by Strictly Totally Positive and Oscillatory matrices. In the present paper we investigate how these spectral properties are related with those characterizing the correlation matrices considered, i.e. the positivity and the monotonicity of their elements. On the basis of these relations we prove the simplicity of the first two eigenvalues and provide an estimate of the second one.

Suggested Citation

  • Ernesto Salinelli & Carlo Sgarra, 2005. "Correlation Matrices of yields and Total Positivity," Working Papers 109, SEMEQ Department - Faculty of Economics - University of Eastern Piedmont.
    • Handle: RePEc:upo:upopwp:109
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    References listed on IDEAS

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    1. Kotz, Samuel & Pearn, W. L. & Wichern, Dean W., 1984. "Eigenvalue-eigenvector analysis for a class of patterned correlation matrices with an application," Statistics & Probability Letters, Elsevier, vol. 2(3), pages 119-125, May.
    2. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
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