On Conditional Moments of GARCH Models, with Applications to Multiple Period Value at Risk Estimation

Institute of Statistical Science, Academia Sinica & International Chinese Statistical Association
Publication Type:
Journal Article
Statistica Sinica, 2003, 13 (4), pp. 1015 - 1044
Issue Date:
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In this article, the exact conditional second and fourth moments of returns and their temporal aggregates are derived under GARCH models. Three multiple period Value at Risk estimation methods are proposed. Two methods are based on the exact second and fourth moments and the other adopts a Monte Carlo approach. Some simulations show that the multiple period Value at Risk calculated from a tdistribution with the variance and the degrees of freedom chosen to match the second and fourth moments of the aggregate returns is close to the one obtained by Monte Carlo simulations. Using some market indices for illustration, the proposed Value at Risk estimation methods are found to be superior to some standard approaches such as RiskMetrics.
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