Scandinavian Working Papers in Economics

Working Papers,
Lund University, Department of Economics

No 2000:14: Orthogonal GARCH and Covariance Matrix Forecasting in a Stress Scenario: The Nordic Stock Markets During the Asian Financial Crisis 1997-1998

Hans Byström ()
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Hans Byström: Department of Economics, Lund University, Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund, Sweden

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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