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arXiv · 2111.12640

Completing correlation matrices

Olaf Dreyer·Horst Köhler·Thomas Streuer
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Abstract

We describe a way to complete a correlation matrix that is not fully specified. Such matrices often arise in financial applications when the number of stochastic variables becomes large or when several smaller models are combined in a larger model. We argue that the proper completion to consider is the matrix that maximizes the entropy of the distribution described by the matrix. We then give a way to construct this matrix starting from the graph associated with the incomplete matrix. If this graph is chordal our construction will result in a proper correlation matrix. We give a detailed description of the construction for a cross-currency model with six stochastic variables and describe extensions to larger models involving more currencies.

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Olaf Dreyer, Horst Köhler, Thomas Streuer. 2021-11-24. Completing correlation matrices. https://arxiv.org/abs/2111.12640

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