Evaluating the predictive accuracy of volatility models

Standard statistical loss functions, such as mean-squared error, are common ly used for evaluating financial volatility forecasts. In this paper, an al ternative evaluation framework, based on probability scoring rules that can be more closely tailored to a forecast user's decision problem, is propose d. According to the decision at hand, the user specifies the economic event s to be forecast, the scoring rule with which to evaluate these probability forecasts, and the subsets of the forecasts of particular interest. The vo latility forecasts from a model are then transformed into probability forec asts of the relevant events and evaluated using the selected scoring rule a nd calibration tests. An empirical example using exchange rate data illustr ates the framework and confirms that the choice of loss function directly a ffects the forecast evaluation results. Copyright (C) 2001 John Wiley & Son s, Ltd.