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Rank reduction of correlation matrices by majorization

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Author Info

  • Raoul Pietersz
  • Patrick Groenen

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. Such an application mainly concerns interest rates.

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File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680400016182
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Bibliographic Info

Article provided by Taylor and Francis Journals in its journal Quantitative Finance.

Volume (Year): 4 (2004)
Issue (Month): 6 ()
Pages: 649-662

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Handle: RePEc:taf:quantf:v:4:y:2004:i:6:p:649-662

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References

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  1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
  2. 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.
  3. 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.
  4. Grubišić, I. & Pietersz, R., 2005. "Efficient Rank Reduction of Correlation Matrices," Research Paper 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.
  5. Henk Kiers & Patrick Groenen, 1996. "A monotonically convergent algorithm for orthogonal congruence rotation," Psychometrika, Springer, vol. 61(2), pages 375-389, June.
  6. Willard I. Zangwill, 1969. "Convergence Conditions for Nonlinear Programming Algorithms," Management Science, INFORMS, vol. 16(1), pages 1-13, September.
  7. Groenen, P.J.F. & Velden, M. van de, 2004. "Multidimensional scaling," Econometric Institute Report EI 2004-15, Erasmus University Rotterdam, Econometric Institute.
  8. 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.
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Citations

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Cited by:
  1. Raoul Pietersz & Antoon Pelsser, 2005. "A Comparison of Single Factor Markov-functional and Multi Factor Market Models," Finance 0502008, EconWPA.
  2. Pietersz, R. & Regenmortel, M. van, 2005. "Generic Market Models," Research Paper 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.
  3. 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.
  4. 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.
  5. 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.
  6. Hebert, Pierre-Alexandre & Masson, Marie-Helene & Denoeux, Thierry, 2006. "Fuzzy multidimensional scaling," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 335-359, November.
  7. 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.

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