Rank Reduction of Correlation Matrices by Majorization
AbstractA 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.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0502006.
Length: 29 pages
Date of creation: 11 Feb 2005
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Note: Type of Document - pdf; pages: 29
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rank; correlation matrix; majorization; lognormal price processes;
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.
- Pietersz, R. & Groenen, P.J.F., 2004. "Rank reduction of correlation matrices by majorization," Econometric Institute Report EI 2004-11, Erasmus University Rotterdam, Econometric Institute.
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-04-16 (All new papers)
- NEP-CMP-2005-04-16 (Computational Economics)
- NEP-FIN-2005-04-16 (Finance)
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