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. Such an application mainly concerns interest rates.
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Bibliographic InfoArticle provided by Taylor and Francis Journals in its journal Quantitative Finance.
Volume (Year): 4 (2004)
Issue (Month): 6 ()
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Web page: http://taylorandfrancis.metapress.com/link.asp?target=journal&id=111405
Other versions of this item:
- 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.
- 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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