Computing a Nearest Correlation Matrix with Factor Structure

Computing a Nearest Correlation Matrix with Factor Structure

An n×n correlation matrix has k factor structure if its off-diagonal agrees with that of a rank k matrix. Such correlation matrices arise, for example, in factor models of collateralized debt obligations (CDOs) and multivariate time series. We analyze the properties of these matrices and, in particular, obtain an explicit formula for the rank in the one factor case. Our main focus is on the nea...

Computing the Nearest Correlation Matrix

Computing the Nearest Correlation Matrix—A Problem from Finance

Given a symmetric matrix what is the nearest correlation matrix, that is, the nearest symmetric positive semidefinite matrix with unit diagonal? This problem arises in the finance industry, where the correlations are between stocks. For distance measured in two weighted Frobenius norms we characterize the solution using convex analysis. We show how the modified alternating projections method ca...

Block relaxation and majorization methods for the nearest correlation matrix with factor structure

We propose two numerical methods, namely the block relaxation and majorization method, for the problem of nearest correlation matrix with factor structure, which is highly nonconvex. In the block relaxation method, the subproblem is of the standard trust region problem, which is solved by Steighaug’s truncated conjugate gradient method or by the trust region method of [21]. In the majorization ...

Computing the Nearest Correlation Matrix using Difference Map Algorithm

The difference map algorithm (DMA) is originally designed to find the global optimal solution to nonconvex problems. The main feature of DMA is that it can avoid the stagnation, (which always occurs when applying the alternating projection method (APM) on nonconvex problems so that APM is trapped at local minimized point and fail to find the global optimal solution.) and converge to the global ...