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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)

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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://129.3.20.41/eps/fin/papers/0502/0502006.pdf
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Publisher 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://129.3.20.41

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

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Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Groenen, P.J.F. & Velden, M. van de, 2004. "Multidimensional scaling," Econometric Institute Report EI 2004-15 Revision_Date:, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
  2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330. [Downloadable!] (restricted)
  3. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March. [Downloadable!] (restricted)
    Other versions:
  4. 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. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
  6. Henk Kiers & Patrick Groenen, 1996. "A monotonically convergent algorithm for orthogonal congruence rotation," Psychometrika, Springer, vol. 61(2), pages 375-389, June. [Downloadable!] (restricted)
  7. Igor Grubisic & Raoul Pietersz, 2005. "Efficient Rank Reduction of Correlation Matrices," Finance 0502007, EconWPA. [Downloadable!]
    Other versions:
    • GrubiÅ¡ić, I. & Pietersz, R., 2005. "Efficient Rank Reduction of Correlation Matrices," Research Paper ERS-2005-009-F&A Revision, 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. [Downloadable!]
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, EconWPA. [Downloadable!]
    Other versions:
    • Pietersz, R. & Regenmortel, M. van, 2005. "Generic Market Models," Research Paper ERS-2005-010-F&A Revision, 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. [Downloadable!]
  2. 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. [Downloadable!]
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