Modeling and forecasting the volatility of Brazilian asset returns

The goal of this paper is twofold. First, using five of the most actively traded stocks in the Brazilian financial market, this paper shows that the normality assumption commonly used in the risk management area to describe the distributions of returns standardized by volatilities is not compatible with volatilities estimated by EWMA or GARCH models. In sharp contrast, when the information contained in high frequency data is used to construct the realized volatility measures, we attain the normality of the standardized returns, giving promise of improvements in Value-at-Risk statistics. We also describe the distributions of volatilities of the Brazilian stocks, showing that they are nearly lognormal. Second, we estimate a simple model to the log of realized volatilities that differs from the ones in other studies. The main difference is that we do not find evidence of long memory. The estimated model is compared with commonly used alternatives in an out-of-sample forecasting experiment.