Working Papers,
Lund University, Department of Economics

Abstract: In Risk Management, modelling large numbers of assets and their variances and covariances together 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. In this article, I therefore assess 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, I find Orthogonal GARCH to perform significantly better than traditional historical variance and moving average methods. As out of sample evaluation measures, I use 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".

Keywords: principal components; multivariate GARCH; covariance matrix; forecast evaluation.

JEL-codes: C32; C53; G15; G19

25 pages, September 28, 2000

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Published as

Hans Byström, (2004), 'Orthogonal GARCH and Covariance Matrix Forecasting in a Stress Scenario: The Nordic Stock Markets During the Asian Financial Crisis 1997-1998', European Journal of Finance, vol 10, no 1, pages 44-67

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