Efficient Rank Reduction of Correlation Matrices
AbstractGeometric 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.
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Bibliographic InfoPaper provided by Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam in its series ERIM Report Series Research in Management with number ERS-2005-009-F&A.
Date of creation: 03 Apr 2005
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LIBOR market model; Rank; correlation matrix; geometric optimisation;
Other versions of this item:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G3 - Financial Economics - - Corporate Finance and Governance
- M - Business Administration and Business Economics; Marketing; Accounting
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