Rehabilitation of improper correlation matrices
نویسندگان
چکیده
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 on 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 the Cholesky factorisation, and its mode constitutes the new proper correlation matrix. The optimisation is complemented by a visual representations of the entries that were most affected by the legalisation procedure. We also sketch a Bayesian approach to the same problem. Front page photo © www.clipart.com 2009.
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