IDEAS home Printed from https://ideas.repec.org/p/upo/upopwp/109.html
   My bibliography  Save this paper

Correlation Matrices of yields and Total Positivity

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://semeq.unipmn.it/files/semeq109.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. 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.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Forward rates; Correlation matrices; Principal Component Analysis; Total Positivity;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:upo:upopwp:109. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://edirc.repec.org/data/dspmnit.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.