Improving the Most General Methodology to Create a Valid Correlation Matrix

Jaeckel and Rebonato develop two different methods of creating valid correlation matrices: construction by hypersphere decomposition and by singular value (i.e. spectral) decomposition. Although both methods yield satisfactory results in practice, from a mathematical point of view, they both share some theoretical drawbacks. Using results from semidefinite programming (SDP) we give the most general problem formulation to compute valid correlation matrices. We present numerical results which prove that these SDPs are rather easily solvable with efficient solvers for SDP problems (e.g. PENNON, see [3]). In contrast to Higham we do not find numerical difficulties in solving the stated SDP problems. We close the article with two more very important features which have been neglected in literature so far. First, regularity and second, control of the condition number of the resulting correlation matrix are easily guaranteed by linear SDPconstraints. Numerical experiments show that these additional constraints do not harm the efficient numerical solution.     «

Jaeckel and Rebonato develop two different methods of creating valid correlation matrices: construction by hypersphere decomposition and by singular value (i.e. spectral) decomposition. Although both methods yield satisfactory results in practice, from a mathematical point of view, they both share some theoretical drawbacks. Using results from semidefinite programming (SDP) we give the most general problem formulation to compute valid correlation matrices. We present numerical results which prov...     »