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Orthogonal Methods for Generating Large Positive Semi-Definite Covariance Matrices

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  • Carol Alexander

    (ICMA Centre, University of Reading)

Abstract

It is a common problem in risk management today that risk measures and pricing models are being applied to a very large set of scenarios based on movements in all possible risk factors. The dimensions are so large that the computations become extremely slow and cumbersome, so it is quite common that over-simplistic assumptions will be made. In particular, in order to generate the large covariance matrices that are used in Value-at-Risk models, some very strong constraints are imposed on the movements in volatility and correlations in all the standard models. The constant volatility assumption is also imposed, because it has not been possible to generate large GARCH covariance matrices with mean-reverting term structures.

Suggested Citation

  • Carol Alexander, 2000. "Orthogonal Methods for Generating Large Positive Semi-Definite Covariance Matrices," ICMA Centre Discussion Papers in Finance icma-dp2000-06, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2000-06
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    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2000-06.pdf
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    References listed on IDEAS

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    2. Marshall, Andrew & Maulana, Tubagus & Tang, Leilei, 2009. "The estimation and determinants of emerging market country risk and the dynamic conditional correlation GARCH model," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 250-259, December.
    3. Aboura, Sofiane & Chevallier, Julien, 2015. "Cross-market volatility index with Factor-DCC," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 132-140.
    4. Aboura, Sofiane & Chevallier, Julien, 2014. "Cross-market index with Factor-DCC," Economic Modelling, Elsevier, vol. 40(C), pages 158-166.
    5. Borgsen, Sina & Glaser, Markus, 2005. "Diversifikationseffekte durch Small und Mid Caps?," Sonderforschungsbereich 504 Publications 05-10, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    6. Sébastien Laurent & Jeroen V. K. Rombouts & Francesco Violante, 2012. "On the forecasting accuracy of multivariate GARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 934-955, September.
    7. Aboura, Sofiane & Chevallier, Julien, 2015. "A cross-volatility index for hedging the country risk," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 38(C), pages 25-41.
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    10. Laurent, Sébastien & Rombouts, Jeroen V.K. & Violante, Francesco, 2013. "On loss functions and ranking forecasting performances of multivariate volatility models," Journal of Econometrics, Elsevier, vol. 173(1), pages 1-10.
    11. Aboura, Sofiane & Chevallier, Julien, 2015. "Geographical diversification with a World Volatility Index," Journal of Multinational Financial Management, Elsevier, vol. 30(C), pages 62-82.
    12. Alfredo Trespalacios Carrasquilla & José Miguel Sánchez, 2018. "Sobre la volatilidad de la curva de rendimientos del mercado colombiano de deuda pública," Revista Ecos de Economía, Universidad EAFIT, vol. 22(46), pages 28-59, June.
    13. Borgsen, Sina & Glaser, Markus, 2005. "Diversifikationseffekte durch small und mid caps? : Eine empirische Untersuchung basierend auf europäischen Aktienindizes," Papers 05-10, Sonderforschungsbreich 504.
    14. Panayiotis F. Diamandis & Anastassios A. Drakos & Georgios P. Kouretas & Leonidas P. Zarangas, 2012. "Asset allocation in the Athens stock exchange: a variance sensitivity analysis," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 17(2), pages 167-181, April.
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