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Orthogonal GARCH and covariance matrix forecasting: The Nordic stock markets during the Asian financial crisis 1997-1998

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  • Hans Bystrom

Abstract

In risk management, modelling large numbers of assets and their variances and covariances in a unified framework is often important. In such multivariate frameworks, it is difficult to incorporate GARCH models and thus a new member of the ARCH-family, Orthogonal GARCH, has been suggested as a remedy to inherent estimation problems in multivariate ARCH modelling. Orthogonal GARCH creates positive definite covariance matrices of any size but builds on assumptions that partly break down during stress scenarios. This article therefore assesses the stress performance of the model by looking at four Nordic stock indices and covariance matrix forecasts during the highly volatile years of 1997 and 1998. Overall, Orthogonal GARCH is found to perform significantly better than traditional historical variance and moving average methods. Out-of-sample evaluation measures include symmetric loss functions (RMSE), asymmetric loss functions, operational methods suggested by the Basle Committee on Banking Supervision, as well as a forecast evaluation methodology based on pricing of simulated 'rainbow options'.

Suggested Citation

  • Hans Bystrom, 2004. "Orthogonal GARCH and covariance matrix forecasting: The Nordic stock markets during the Asian financial crisis 1997-1998," The European Journal of Finance, Taylor & Francis Journals, vol. 10(1), pages 44-67.
    • Handle: RePEc:taf:eurjfi:v:10:y:2004:i:1:p:44-67
    DOI: 10.1080/1351847032000061379
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    References listed on IDEAS

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    1. 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.
    2. Robert F. Engle & Che-Hsiung Hong & Alex Kane, 1990. "Valuation of Variance Forecast with Simulated Option Markets," NBER Working Papers 3350, National Bureau of Economic Research, Inc.
    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.
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    Cited by:

    1. Lillie Lam & Laurence Fung & Ip-wing Yu, 2009. "Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes," Working Papers 0901, Hong Kong Monetary Authority.
    2. Alessandro Cardinali, 2012. "An Out-of-sample Analysis of Mean-Variance Portfolios with Orthogonal GARCH Factors," International Econometric Review (IER), Econometric Research Association, vol. 4(1), pages 1-16, April.
    3. Wolfgang Karl Härdle & Sergey Nasekin & David Lee Kuo Chuen & Phoon Kok Fai, 2014. "TEDAS - Tail Event Driven ASset Allocation," SFB 649 Discussion Papers SFB649DP2014-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Chong, James, 2005. "The forecasting abilities of implied and econometric variance-covariance models across financial measures," Journal of Economics and Business, Elsevier, vol. 57(5), pages 463-490.
    5. Marcelo Scherer Perlin & Mauro Mastella & Daniel Francisco Vancin & Henrique Pinto Ramos, 2021. "A GARCH Tutorial with R," RAC - Revista de Administração Contemporânea (Journal of Contemporary Administration), ANPAD - Associação Nacional de Pós-Graduação e Pesquisa em Administração, vol. 25(1), pages 200088-2000.

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