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Statistical rehabilitation of improper correlation matrices

Listed author(s):
  • A. Frigessi
  • A. Løland
  • A. Pievatolo
  • F. Ruggeri
Registered author(s):

    The simplest way to describe the dependence for a set of financial assets is their correlation matrix. This correlation matrix can be improper when it is specified element-wise. We describe a new method for obtaining a positive definite correlation matrix starting from an improper one. The expert's opinion and trust in each pairwise correlation is described by a beta distribution. Then, by combining these individual distributions, a joint distribution over the space of positive definite correlation matrices is obtained using Cholesky factorization, and its mode constitutes the new proper correlation matrix. The optimization is complemented by a visual representation of the entries that were most affected by the legalization procedure. We also sketch a Bayesian approach to the same problem.

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    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 11 (2011)
    Issue (Month): 7 ()
    Pages: 1081-1090

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    Handle: RePEc:taf:quantf:v:11:y:2011:i:7:p:1081-1090
    DOI: 10.1080/14697680903390118
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