IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/2000.html
   My bibliography  Save this paper

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

Author

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/2000/1/MPRA_paper_2000.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/31282/1/MPRA_paper_31282.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    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. 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.
    5. Igor Grubisic & Raoul Pietersz, 2005. "Efficient Rank Reduction of Correlation Matrices," Finance 0502007, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. Ingram Olkin, 1981. "Range restrictions for product-moment correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 469-472, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    3. George J. Jiang & Pieter J. van der Sluis, 1999. "Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates," Review of Finance, European Finance Association, vol. 3(3), pages 273-310.
    4. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    5. Jeonggyu Huh, 2018. "Measuring Systematic Risk with Neural Network Factor Model," Papers 1809.04925, arXiv.org.
    6. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    7. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    8. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    9. Christian Bayer & Chiheb Ben Hammouda & Raul Tempone, 2020. "Multilevel Monte Carlo with Numerical Smoothing for Robust and Efficient Computation of Probabilities and Densities," Papers 2003.05708, arXiv.org, revised Oct 2023.
    10. Roman Horsky & Tilman Sayer, 2015. "Joining The Heston And A Three-Factor Short Rate Model: A Closed-Form Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-17, December.
    11. Jie-Cao He & Hsing-Hua Chang & Ting-Fu Chen & Shih-Kuei Lin, 2023. "Upside and downside correlated jump risk premia of currency options and expected returns," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-58, December.
    12. Jos'e Da Fonseca & Claude Martini, 2014. "The $\alpha$-Hypergeometric Stochastic Volatility Model," Papers 1409.5142, arXiv.org.
    13. Raul Merino & Jan Posp'iv{s}il & Tom'av{s} Sobotka & Tommi Sottinen & Josep Vives, 2019. "Decomposition formula for rough Volterra stochastic volatility models," Papers 1906.07101, arXiv.org, revised Aug 2019.
    14. Annalena Mickel & Andreas Neuenkirch, 2021. "The Weak Convergence Rate of Two Semi-Exact Discretization Schemes for the Heston Model," Risks, MDPI, vol. 9(1), pages 1-38, January.
    15. Denis Belomestny & Stanley Matthew & John Schoenmakers, 2007. "A stochastic volatility Libor model and its robust calibration," SFB 649 Discussion Papers SFB649DP2007-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    17. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
      • 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 University Rotterdam.
      • Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, University Library of Munich, Germany.
    18. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.
    19. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    20. 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.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:2000. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.