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Completing correlation matrices of arbitrary order by differential evolution method of global optimization: A Fortran program

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Abstract

Correlation matrices have many applications, particularly in marketing and financial economics. The need to forecast demand for a group of products in order to realize savings by properly managing inventories requires the use of correlation matrices. In many cases, due to paucity of data/information or dynamic nature of the problem at hand, it is not possible to obtain a complete correlation matrix. Some elements of the matrix are unknown. Several methods exist that obtain valid complete correlation matrices from incomplete correlation matrices. In view of non-unique solutions admissible to the problem of completing the correlation matrix, some authors have suggested numerical methods that provide ranges to different unknown elements. However, they are limited to very small matrices up to order 4. Our objective in this paper is to suggest a method (and provide a Fortran program) that completes a given incomplete correlation matrix of an arbitrary order. The method proposed here has an advantage over other algorithms due to its ability to present a scenario of valid correlation matrices that might be obtained from a given incomplete matrix of an arbitrary order. The analyst may choose some particular matrices, most suitable to his purpose, from among those output matrices. Further, unlike other methods, it has no restriction on the distribution of holes over the entire matrix, nor the analyst has to interactively feed elements of the matrix sequentially, which might be quite inconvenient for larger matrices. It is flexible and by merely choosing larger population size one might obtain a more exhaustive scenario of valid matrices.

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  • 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.
    • Handle: RePEc:pra:mprapa:2000
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    References listed on IDEAS

    as
    1. 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.
    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. Chesney, Marc & Scott, Louis, 1989. "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 267-284, September.
    4. Ingram Olkin, 1981. "Range restrictions for product-moment correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 469-472, December.
    5. 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 University Rotterdam.
    6. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. Mishra, SK, 2006. "Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions," MPRA Paper 1005, University Library of Munich, Germany.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Incomplete; complete; correlation matrix; valid; semi-definite; eigenvalues; Differential Evolution; global optimization; computer program; fortran; financial economics; arbitrary order;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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