Efficient rank reduction of correlation matrices
Copyright policy )Efficient rank reduction of correlation matrices
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.
First version: 20 pages, 4 figures Second version [changed content]: 21 pages, 6 figures
- Utrecht University Netherlands
- ABN AMRO BANK NV Netherlands
LIBOR market model, Rank, correlation matrix, geometric optimisation, Numerical solutions to overdetermined systems, pseudoinverses, geometric optimisation, FOS: Physical sciences, Quadratic programming, Numerical mathematical programming methods, Discrete Mathematics and Combinatorics, geometric optimisation, correlation matrix, rank, LIBOR market model, Correlation matrix, Geometric optimisation, Lagrange multiplier method, numerical examples, Numerical Analysis, Algebra and Number Theory, Rank, LIBOR market model, Condensed Matter - Other Condensed Matter, rank, Landbouwwetenschappen, Wiskunde: algemeen, Natuurwetenschappen, correlation matrix, Geometry and Topology, Mathematics, Other Condensed Matter (cond-mat.other), jel: jel:C61, jel: jel:E43, jel: jel:M, jel: jel:G3, jel: jel:G13
LIBOR market model, Rank, correlation matrix, geometric optimisation, Numerical solutions to overdetermined systems, pseudoinverses, geometric optimisation, FOS: Physical sciences, Quadratic programming, Numerical mathematical programming methods, Discrete Mathematics and Combinatorics, geometric optimisation, correlation matrix, rank, LIBOR market model, Correlation matrix, Geometric optimisation, Lagrange multiplier method, numerical examples, Numerical Analysis, Algebra and Number Theory, Rank, LIBOR market model, Condensed Matter - Other Condensed Matter, rank, Landbouwwetenschappen, Wiskunde: algemeen, Natuurwetenschappen, correlation matrix, Geometry and Topology, Mathematics, Other Condensed Matter (cond-mat.other), jel: jel:C61, jel: jel:E43, jel: jel:M, jel: jel:G3, jel: jel:G13
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