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Rank Reduction of Correlation Matrices by Majorization

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Author Info

  • Raoul Pietersz

    (Erasmus University Rotterdam)

  • Patrick J. F. Groenen

    (Erasmus University Rotterdam)

Abstract

A novel algorithm is developed for the problem of finding a low-rank correlation matrix nearest to a given correlation matrix. The algorithm is based on majorization and, therefore, it is globally convergent. The algorithm is computationally efficient, is straightforward to implement, and can handle arbitrary weights on the entries of the correlation matrix. A simulation study suggests that majorization compares favourably with competing approaches in terms of the quality of the solution within a fixed computational time. The problem of rank reduction of correlation matrices occurs when pricing a derivative dependent on a large number of assets, where the asset prices are modelled as correlated log-normal processes. Mainly, such an application concerns interest rates.

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File URL: http://128.118.178.162/eps/fin/papers/0502/0502006.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0502006.

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Length: 29 pages
Date of creation: 11 Feb 2005
Date of revision:
Handle: RePEc:wpa:wuwpfi:0502006

Note: Type of Document - pdf; pages: 29
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Web page: http://128.118.178.162

Related research

Keywords: rank; correlation matrix; majorization; lognormal price processes;

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References

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  1. Grubisic, I. & Pietersz, R., 2005. "Efficient Rank Reduction of Correlation Matrices," ERIM Report Series Research in Management ERS-2005-009-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 Uni.
  2. Willard I. Zangwill, 1969. "Convergence Conditions for Nonlinear Programming Algorithms," Management Science, INFORMS, vol. 16(1), pages 1-13, September.
  3. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
  4. Alan Brace & Dariusz G´┐Żatarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
  5. 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.
  6. Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
  7. Henk Kiers & Patrick Groenen, 1996. "A monotonically convergent algorithm for orthogonal congruence rotation," Psychometrika, Springer, vol. 61(2), pages 375-389, June.
  8. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
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Citations

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Cited by:
  1. Raoul Pietersz & Antoon Pelsser, 2005. "A Comparison of Single Factor Markov-functional and Multi Factor Market Models," Finance 0502008, EconWPA.
  2. Qingna Li & Houduo Qi & Naihua Xiu, 2011. "Block relaxation and majorization methods for the nearest correlation matrix with factor structure," Computational Optimization and Applications, Springer, vol. 50(2), pages 327-349, October.
  3. Mishra, SK, 2004. "Optimal solution of the nearest correlation matrix problem by minimization of the maximum norm," MPRA Paper 1783, University Library of Munich, Germany.
  4. 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.
  5. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
  6. 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.
  7. 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.
  8. Hebert, Pierre-Alexandre & Masson, Marie-Helene & Denoeux, Thierry, 2006. "Fuzzy multidimensional scaling," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 335-359, November.
  9. Kohei Adachi, 2011. "Constrained principal component analysis of standardized data for biplots with unit-length variable vectors," Advances in Data Analysis and Classification, Springer, vol. 5(1), pages 23-36, April.

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