Rank reduction of correlation matrices by majorization |
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Authors: | Raoul Pietersz Patrick J F Groenen |
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Affiliation: | 1. Erasmus Research Institute of Management , Erasmus University Rotterdam , P.O. Box 1738, 3000 DR Rotterdam, The Netherlands;2. Product Development Group (HQ7011) , ABN AMRO Bank , P.O. Box 283, 1000 EA Amsterdam, The Netherlands;3. Econometric Institute , Erasmus University Rotterdam , P.O. Box 1738, 3000 DR Rotterdam, The Netherlands E-mail: pietersz@few.eur.nl and groenen@few.eur.nl |
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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 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. Such an application mainly concerns interest rates. |
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