Completing Correlation Matrices of Arbitrary Order by Differential Evolution Method of Global Optimization: A Fortran Program

In some cases, the matrix available to the analyst/decision-maker is complete, but it is an invalid (not positive semi-definite) correlation matrix. There could be many reasons that give rise to such invalid matrices (Mishra, 2004). In such cases, the problem is to obtain a positive semi-definite approximate correlation matrix, which, in some sense, is closest to the given invalid matrix. A number of methods have been developed to obtain such nearest correlation matrices. The works of Rebonato and Jäckel (1999), Higham (2002), Anjos et al. (2003), Pietersz and Groenen (2004), Grubisic and Pietersz (2004) and Mishra (2004) are some of them.