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Efficient Rank Reduction of Correlation Matrices

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  • Grubisic, I.
  • Pietersz, R.

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.

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Bibliographic Info

Paper 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.

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Date of creation: 03 Apr 2005
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Handle: RePEc:ems:eureri:1933

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Postal: RSM Erasmus University & Erasmus School of Economics, PoBox 1738, 3000 DR Rotterdam
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Web page: http://www.erim.eur.nl/
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Keywords: LIBOR market model; Rank; correlation matrix; geometric optimisation;

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References

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  1. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
  2. Jong, F.C.J.M. de & Driessen, J. & Pelsser, A., 2004. "On the information in the interest rate term structure and option prices," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3159390, Tilburg University.
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Citations

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Cited by:
  1. Massimo Morini & Nick Webber, 2006. "An EZI Method to Reduce the Rank of a Correlation Matrix in Financial Modelling," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(4), pages 309-331.
  2. Pietersz, R. & Pelsser, A.A.J., 2005. "A Comparison of Single Factor Markov-Functional and Multi Factor Market Models," ERIM Report Series Research in Management ERS-2005-008-F&A, 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.
  3. Raoul Pietersz & Patrick J. F. Groenen, 2005. "Rank Reduction of Correlation Matrices by Majorization," Finance 0502006, EconWPA.
  4. Sudhanshu K Mishra, 2013. "Global Optimization of Some Difficult Benchmark Functions by Host-Parasite Coevolutionary Algorithm," Economics Bulletin, AccessEcon, vol. 33(1), pages 1-18.
  5. Mishra, SK, 2007. "Completing correlation matrices of arbitrary order by differential evolution method of global optimization: A Fortran program," MPRA Paper 2000, University Library of Munich, Germany.
  6. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
  7. Ken-ichi Mitsui & Yoshio Tabata, 2006. "Random Correlation Matrix and De-Noising," Discussion Papers in Economics and Business 06-26, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).
  8. Aleksei Minabutdinov & Ilia Manaev & Maxim Bouev, 2014. "Finding The Nearest Valid Covariance Matrix: A Fx Market Case," HSE Working papers WP BRP 32/FE/2014, National Research University Higher School of Economics.
  9. Shujun Bi & Le Han & Shaohua Pan, 2013. "Approximation of rank function and its application to the nearest low-rank correlation matrix," Journal of Global Optimization, Springer, vol. 57(4), pages 1113-1137, December.

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