Evaluation of volatility predictions in a VaR framework

The evaluation of volatility forecasts is not straightforward and some issues can arise. A standard approach relies on statistical loss functions. Another approach bases the evaluation of the volatility predictions on utility functions or Value at Risk (VaR) measures. This work aims to combine the two approaches, using the VaR measures within the loss functions. By means of this method, the VaR measures obtained from a set of competing models are plugged into two loss functions, the magnitude loss function and a proposed new one. This latter loss function more heavily penalizes the models with a number of VaR violations greater than the expected one. The loss function values are evaluated against a benchmark obtained from the inclusion of a consistent estimate of the VaR measures in the loss function. In order to investigate the performance of the proposed method and the new loss function, a Monte Carlo experiment and an empirical analysis of a stock listed on the New York Stock Exchange are provided. The proposed strategy helps with the selection of a superior model, in terms of forecast accuracy, when the cited approaches do not clearly and uniquely identify it. Moreover, the new asymmetric loss function allows a greater discrimination with regard to models, helping to find the best volatility model.