2021/11/24 by Dreyer, Olaf, Köhler, Horst, Streuer, Thomas
#15A15 #15A83 (Primary) 15A10 #15B48 (Secondary) #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)
paper · doi:10.48550/arxiv.2111.12640
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.