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Efficient Rank Reduction of Correlation Matrices

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Author Info
Igor Grubisic (Utrecht University)
Raoul Pietersz (Erasmus University Rotterdam)

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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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File URL: http://129.3.20.41/eps/fin/papers/0502/0502007.pdf
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Paper provided by EconWPA in its series Finance with number 0502007.

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Length: 21 pages
Date of creation: 11 Feb 2005
Date of revision:
Handle: RePEc:wpa:wuwpfi:0502007

Note: Type of Document - pdf; pages: 21
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Web page: http://129.3.20.41

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Keywords: geometric optimisation; correlation matrix; rank; LIBOR market model;

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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. 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!]
  2. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 16(3), pages 631-678, July. [Downloadable!] (restricted)
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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. 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). [Downloadable!]
  3. Massimo Morini & Nick Webber, 2006. "An EZI Method to Reduce the Rank of a Correlation Matrix in Financial Modelling," Applied Mathematical Finance, Taylor and Francis Journals, vol. 13(4), pages 309-331, December. [Downloadable!] (restricted)
  4. Raoul Pietersz & Patrick J. F. Groenen, 2005. "Rank Reduction of Correlation Matrices by Majorization," Finance 0502006, EconWPA. [Downloadable!]
    Other versions:
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