Evaluating the predictive accuracy of volatility models

The volatility forecast evaluations most meaningful to forecast users are those conducted under economically relevant loss functions. Although several such loss functions are proposed in the literature, their implied economic costs are of interest only to specific types of volatility forecast users. A forecast evaluation framework that incorporates a more general class of economic loss functions is proposed. A user's loss function specifies the three key elements of the evaluation framework: the economic events to be forecast, the criterion with which to evaluate these forecasts, and the subsets of the forecasts of particular interest. Volatility forecasts are transformed into probability forecasts of the specified events, and the probability forecasts are evaluated using statistical criteria, such as probability scoring rules, tailored to the user's interests. An empirical example using exchange rates illustrates the procedure and confirms that the choice of loss function directly affects the forecast evaluation results.