In this paper a novel method is developed for the problem of finding a low-rank correlation matrix nearest to a given correlation matrix. The method is based on majorization and therefore it is globally convergent. The method is computationally efficient, is straightforward to implement, and can handle arbitrary weights on the entries of the correlation matrix. A simulation study suggests that majorization compares favourably with competing approaches in terms of the quality of the solution within a fixed computational time. The problem of rank reduction of correlation matrices occurs when pricing a derivative dependent on a large number of assets, where the asset prices are modelled as correlated log-normal processes.

correlation matrix, lognormal price processes, majorization, rank
Contingent Pricing; Futures Pricing (jel G13)
hdl.handle.net/1765/1202
Econometric Institute Research Papers
Erasmus School of Economics

Pietersz, R, & Groenen, P.J.F. (2004). Rank reduction of correlation matrices by majorization (No. EI 2004-11). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/1202