Rank Reduction of Correlation Matrices by Majorization

A novel algorithm is developed for the problem of finding a low-rank correlation matrix nearest to a given correlation matrix. The algorithm is based on majorization and, therefore, it is globally convergent. The algorithm 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. Mainly, such an application concerns interest rates.