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.

LIBOR market model, Rank, correlation matrix, geometric optimisation
Optimization Techniques; Programming Models; Dynamic Analysis (jel C61), Determination of Interest Rates; Term Structure of Interest Rates (jel E43), Contingent Pricing; Futures Pricing (jel G13), Corporate Finance and Governance (jel G3), Business Administration and Business Economics; Marketing; Accounting (jel M)
hdl.handle.net/1765/1933
ERIM Report Series Research in Management
ERIM report series research in management Erasmus Research Institute of Management
Erasmus Research Institute of Management

Grubisic, I, & Pietersz, R. (2005). Efficient Rank Reduction of Correlation Matrices (No. ERS-2005-009-F&A). ERIM report series research in management Erasmus Research Institute of Management. Retrieved from http://hdl.handle.net/1765/1933