Rank reduction of correlation matrices by majorization
AbstractIn 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.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2004-11.
Date of creation: 01 Apr 2004
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correlation matrix; lognormal price processes; majorization; rank;
Other versions of this item:
- Raoul Pietersz & Patrick Groenen, 2004. "Rank reduction of correlation matrices by majorization," Quantitative Finance, Taylor and Francis Journals, vol. 4(6), pages 649-662.
- Raoul Pietersz & Patrick J. F. Groenen, 2005. "Rank Reduction of Correlation Matrices by Majorization," Finance 0502006, EconWPA.
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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