IDEAS home Printed from https://ideas.repec.org/p/rdg/icmadp/icma-dp2000-06.html
   My bibliography  Save this paper

Orthogonal Methods for Generating Large Positive Semi-Definite Covariance Matrices

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2000-06.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. Dimson, Elroy & Marsh, Paul, 1990. "Volatility forecasting without data-snooping," Journal of Banking & Finance, Elsevier, vol. 14(2-3), pages 399-421, August.
    3. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    4. Brailsford, Timothy J. & Faff, Robert W., 1996. "An evaluation of volatility forecasting techniques," Journal of Banking & Finance, Elsevier, vol. 20(3), pages 419-438, April.
    5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. 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.
    2. 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.
    3. Płuciennik Piotr, 2012. "Influence of the American Financial Market on Other Markets During the Subprime Crisis," Folia Oeconomica Stetinensia, Sciendo, vol. 12(2), pages 19-30, December.
    4. Sofiane Aboura & Julien Chevallier, 2014. "The cross-market index for volatility surprise," Journal of Asset Management, Palgrave Macmillan, vol. 15(1), pages 7-23, February.
    5. 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.
    6. Aboura, Sofiane & Chevallier, Julien, 2015. "Geographical diversification with a World Volatility Index," Journal of Multinational Financial Management, Elsevier, vol. 30(C), pages 62-82.
    7. Aboura, Sofiane & Chevallier, Julien, 2014. "Cross-market index with Factor-DCC," Economic Modelling, Elsevier, vol. 40(C), pages 158-166.
    8. 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.
    9. 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.
    10. Aboura, Sofiane & Chevallier, Julien, 2015. "Cross-market volatility index with Factor-DCC," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 132-140.
    11. 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.
    12. Borgsen, Sina & Glaser, Markus, 2005. "Diversifikationseffekte durch small und mid caps? : Eine empirische Untersuchung basierend auf europäischen Aktienindizes," Papers 05-10, Sonderforschungsbreich 504.
    13. 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.

    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. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    2. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, January.
    3. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    4. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    5. Resende, Paulo Angelo Alves & Dorea, Chang Chung Yu, 2016. "Model identification using the Efficient Determination Criterion," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 229-244.
    6. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    7. Kuper, Gerard H. & Lestano, 2007. "Dynamic conditional correlation analysis of financial market interdependence: An application to Thailand and Indonesia," Journal of Asian Economics, Elsevier, vol. 18(4), pages 670-684, August.
    8. Pandey, Ajay, 2003. "Modeling and Forecasting Volatility in Indian Capital Markets," IIMA Working Papers WP2003-08-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    9. Nelson, Daniel B., 1996. "Asymptotic filtering theory for multivariate ARCH models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 1-47.
    10. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    11. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    12. Elena Andreou & Eric Ghysels, 2002. "Tests for Breaks in the Conditional Co-movements of Asset Returns," CIRANO Working Papers 2002s-59, CIRANO.
    13. Eduardo Ramos-P'erez & Pablo J. Alonso-Gonz'alez & Jos'e Javier N'u~nez-Vel'azquez, 2021. "Multi-Transformer: A New Neural Network-Based Architecture for Forecasting S&P Volatility," Papers 2109.12621, arXiv.org.
    14. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    15. Jon Wongswan, 2003. "Contagion: an empirical test," International Finance Discussion Papers 775, Board of Governors of the Federal Reserve System (U.S.).
    16. Audrone Virbickaite & M. Concepción Ausín & Pedro Galeano, 2015. "Bayesian Inference Methods For Univariate And Multivariate Garch Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 76-96, February.
    17. Sinha, Bhaskar, 2007. "Modeling Stock Market Volatility in Emerging Markets: Evidence from India," MPRA Paper 102455, University Library of Munich, Germany, revised 2009.
    18. Sadorsky, Perry, 2006. "Modeling and forecasting petroleum futures volatility," Energy Economics, Elsevier, vol. 28(4), pages 467-488, July.
    19. Mircea ASANDULUI, 2012. "A Multi-Horizon Comparison Of Volatility Forecasts: An Application To Stock Options Traded At Euronext Exchange Amsterdam," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 10, pages 179-190, December.
    20. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.

    More about this item

    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:rdg:icmadp:icma-dp2000-06. 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: Marie Pearson (email available below). General contact details of provider: https://edirc.repec.org/data/bsrdguk.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.