Efficient Rank Reduction of Correlation Matrices

24 Pages Posted: 29 Mar 2006

See all articles by Igor Grubisic

Igor Grubisic

Utrecht University - Faculty of Mathematics and Computer Science

Raoul Pietersz

ABN AMRO

Date Written: April 3, 2005

Abstract

Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with the Lagrange multiplier method is established, along with an identification of whether a local minimum is a global minimum. An additional benefit of the geometric approach is that any weighted norm can be applied. The problem of finding the nearest low-rank correlation matrix occurs as part of the calibration of multi-factor interest rate market models to correlation.

Keywords: geometric optimisation, correlation matrix, Rank, LIBOR market model

Keywords: Geometric optimisation, Correlation matrix, Rank, LIBOR market model

JEL Classification: M, G3, C61, G13, E43

Suggested Citation

Grubisic, Igor and Pietersz, Raoul, Efficient Rank Reduction of Correlation Matrices (April 3, 2005). ERIM Report Series Reference No. ERS-2005-009-F&A. Available at SSRN: https://ssrn.com/abstract=881652

Igor Grubisic (Contact Author)

Utrecht University - Faculty of Mathematics and Computer Science ( email )

Utrecht
Netherlands

Raoul Pietersz

ABN AMRO ( email )

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