When dealing with market risk under the Basel II Accord, variation pays in the form of lower
capital requirements and higher profits. Typically, GARCH type models are chosen to
forecast Value-at-Risk (VaR) using a single risk model. In this paper we illustrate two useful
variations to the standard mechanism for choosing forecasts, namely: (i) combining different
forecast models for each period, such as a daily model that forecasts the supremum or infinum
value for the VaR; (ii) alternatively, select a single model to forecast VaR, and then modify
the daily forecast, depending on the recent history of violations under the Basel II Accord. We
illustrate these points using the Standard and Poor's 500 Composite Index. In many cases we
find significant decreases in the capital requirements, while incurring a number of violations
that stays within the Basel II Accord limits.
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