Statistical rehabilitation of improper correlation matrices

A. Frigessi, A. Løland, A. Pievatolo and F. Ruggeri

Quantitative Finance, 2011, vol. 11, issue 7, 1081-1090

Abstract: 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.

Keywords: Bayesian statistics; Statistics; Correlation; Beta distribution (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1080/14697680903390118

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