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Rank Reduction of Correlation Matrices by Majorization

  • Raoul Pietersz

    (Erasmus University Rotterdam)

  • Patrick J. F. Groenen

    (Erasmus University Rotterdam)

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://econwpa.repec.org/eps/fin/papers/0502/0502006.pdf
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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
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Henk Kiers & Patrick Groenen, 1996. "A monotonically convergent algorithm for orthogonal congruence rotation," Psychometrika, Springer, vol. 61(2), pages 375-389, June.
  2. Frank de Jong & Joost Driessen & Antoon Pelsser, 2004. "On the Information in the Interest Rate Term Structure and Option Prices," Review of Derivatives Research, Springer, vol. 7(2), pages 99-127, 08.
  3. 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 University Rotterdam.
  4. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
  5. 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.
  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. 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.
  8. Willard I. Zangwill, 1969. "Convergence Conditions for Nonlinear Programming Algorithms," Management Science, INFORMS, vol. 16(1), pages 1-13, September.
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