Future volatility forecasting intrigues many scholars, researchers, and people from the financial markets. The model and methodology used for forecasting are fundamental for asset pricing in general, since future volatility deeply influences the final result. Thus, this study uses databases from the companies Vale and Petrobrás, in the period from July 1994 to August 2013, to test the Univariate, Bivariate, GARCH, and EGARCH models (also analyzing the results for the linear and quadratic methods) in order to assess the best model for forecasting future volatility. The results indicate that the quadratic method can better forecast future volatility than the linear method. The Univariate model showed the best results, proving that it is more efficient to use only short-term volatility for future volatility forecasting. If it were necessary to include long-term volatility, the Bivariate model would be the best, despite the GARCH and EGARCH models showing similar results.