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Completing correlation matrices

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  • Olaf Dreyer
  • Horst Kohler
  • Thomas Streuer

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 Kohler & Thomas Streuer, 2021. "Completing correlation matrices," Papers 2111.12640, arXiv.org.
    • Handle: RePEc:arx:papers:2111.12640
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    File URL: http://arxiv.org/pdf/2111.12640
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