Rank reduction of correlation matrices by majorization
AbstractA 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. Such an application mainly concerns interest rates.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Quantitative Finance.
Volume (Year): 4 (2004)
Issue (Month): 6 ()
Contact details of provider:
Web page: http://www.tandfonline.com/RQUF20
Other versions of this item:
- Raoul Pietersz & Patrick J. F. Groenen, 2005. "Rank Reduction of Correlation Matrices by Majorization," Finance 0502006, EconWPA.
- Pietersz, R. & Groenen, P.J.F., 2004. "Rank reduction of correlation matrices by majorization," Econometric Institute Research Papers EI 2004-11, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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.:
- Igor Grubisic & Raoul Pietersz, 2005.
"Efficient Rank Reduction of Correlation Matrices,"
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Alan Brace & Dariusz G�atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
- Henk Kiers & Patrick Groenen, 1996. "A monotonically convergent algorithm for orthogonal congruence rotation," Psychometrika, Springer, vol. 61(2), pages 375-389, June.
- Willard I. Zangwill, 1969. "Convergence Conditions for Nonlinear Programming Algorithms," Management Science, INFORMS, vol. 16(1), pages 1-13, September.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- 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.
- Raoul Pietersz & Antoon Pelsser, 2005. "A Comparison of Single Factor Markov-functional and Multi Factor Market Models," Finance 0502008, EconWPA.
- Pietersz, R. & Pelsser, A.A.J., 2005. "A Comparison of Single Factor Markov-Functional and Multi Factor Market Models," ERIM Report Series Research in Management ERS-2005-008-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.
- 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.
- 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.
- Raoul Pietersz & Marcel van Regenmortel, 2005.
"Generic Market Models,"
- Pietersz, R. & van Regenmortel, M., 2005. "Generic Market Models," ERIM Report Series Research in Management ERS-2005-010-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.
- 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.
- 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.
- Hebert, Pierre-Alexandre & Masson, Marie-Helene & Denoeux, Thierry, 2006. "Fuzzy multidimensional scaling," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 335-359, November.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty).
If references are entirely missing, you can add them using this form.