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Efficient Rank Reduction of Correlation Matrices

Author

Listed:
  • Igor Grubisic

    (Utrecht University)

  • Raoul Pietersz

    (Erasmus University Rotterdam)

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.

Suggested Citation

  • Igor Grubisic & Raoul Pietersz, 2005. "Efficient Rank Reduction of Correlation Matrices," Finance 0502007, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0502007
    Note: Type of Document - pdf; pages: 21
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    References listed on IDEAS

    as
    1. Raoul Pietersz & Patrick Groenen, 2004. "Rank reduction of correlation matrices by majorization," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 649-662.
    2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    3. 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.
    4. 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 409-430, March.
    5. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
    6. Alan Brace & Dariusz G¬łatarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
    7. 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, August.
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    Citations

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    Cited by:

    1. Xiaojing Zhu, 2017. "A Riemannian conjugate gradient method for optimization on the Stiefel manifold," Computational Optimization and Applications, Springer, vol. 67(1), pages 73-110, May.
    2. Raoul Pietersz & Patrick Groenen, 2004. "Rank reduction of correlation matrices by majorization," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 649-662.
    3. 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.
    4. Raoul Pietersz & Antoon Pelsser, 2010. "A comparison of single factor Markov-functional and multi factor market models," Review of Derivatives Research, Springer, vol. 13(3), pages 245-272, October.
    5. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    10. 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.

    More about this item

    Keywords

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

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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