Efficient Rank Reduction of Correlation Matrices 1
Raoul Pietersz, Patrick J. F. Groenen · 2003
Abstract. 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 algo-rithm is computationally efficient, is straightforward to implement, and can handle arbitrary weights on the entries of the correlation matrix. A simula-tion study suggests that majorization compares favourably with competing approaches in terms of the quality of the solution within a fixed computa-tional 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. Key words: rank, correlation matrix, majorization, lognormal price pro-cesses