Evaluation of Volatility Forecasts

The modelization of risk is a hard task for many financial institutions. This explains the great interest for the volatility models during last decades. In this framework, the volatility predictions deriving from a set of models is a partly unexplored research field. A general formulation of this problem involves the volatility proxy, the forecasting models, the forecasting scheme used to generate the predictions and the function employed to evaluate the forecasts. In this thesis, the volatility proxy is the realized volatility while the forecasting models are the (univariate and multivariate) GARCH models and the models that re-parametrize the realized volatility. This work aims to investigate the performance of a set of competing models in terms of volatility forecast accuracy. Generally, the volatility predictions are compared cross-sectionally among the models and with respect to the volatility proxy, by means of statistical and economic approaches. The statistical approach considers the loss function (such as the MSE, RMSE, and so forth). The economic approach uses some indirect risk measures like the Value at Risk (VaR). From the univariate point of view, the statistical and economic approaches are merged. The evaluation of the VaR measures is done through two loss functions, of which one is a new asymmetric loss function. The term asymmetric means that a model with an actual number of violations greater than the expected one is more penalized. The research questions are: (i) Is it possible to use the loss function in a VaR framework in order to evaluate the volatility predictions of a set of competing models? Does this approach bring an advantage when the statistical and the economic approaches fail to recognize the best model? (ii) Is it possible to find a threshold that discriminates low from high loss function values in order to evaluate the performances of the volatility models? The answers are given by using a Monte Carlo simulation and an empirical analysis. From the multivariate point of view, again the two approaches are considered but this time are explicitly compared. The research questions are: (i) Is the ranking of the competing models the same if a statistical and an economic loss functions are used? (ii) Do the multivariate GARCH models have a worse forecast accuracy than that of the models that use the realized volatility to forecast the volatility? The research questions are answered by a Monte Carlo experiment. [edited by Author]