Simulating realistic correlation matrices for financial applications: correlation matrices with the Perron–Frobenius property

Abstract

ABSTRACTThis article is concerned with the simulation of correlation matrices with realistic properties for financial applications. Previous studies found that the major part of observed correlation matrices in financial applications exhibits the Perron-Frobenius property, namely a dominant eigenvector with only positive entries. We present a simulation algorithm for random correlation matrices satisfying this property, which can be augmented to take into account a realistic eigenvalue structure. From the construction principle applied in our algorithm, and the fact that it is able to generate all such correlation matrices, we are further able to prove that the proportion of Perron-Frobenius correlation matrices in the set of all correlation matrices is in dimension d.