The volatility of a financial time series is a key variable in the modeling of the financial markets. It controls the risk measure associated with the dynamics of price of a financial asset and also affects the rational price of derivative products. The volatility of a financial asset is a statistical quantity that describes the characteristic magnitude of price changes of the asset. On the other hand, there is empirical evidence that volatility itself follows a stochastic process underlined to the price process. In this thesis, we investigate the historical series of IBOVESPA. Different methodologies were used to estimate volatility from the empirical data of the fluctuation of the index of prices. In each case, we compare the probability density function (pdf) of daily historical volatility with the theoretical results from several stochastic volatility models proposed in the financial literature. The models considered here describe mean reverting stochastic processes. The associated stochastic differential Itô equations have three parameters: two parameters controlling the mean reverting process (the long run volatility mean and the time rate of reversion of the fluctuations to this mean) and one parameter describing the amplitude of a diffusive Wiener process. The stationary pdfs of the models are obtained through tests of hypothesis. From these results, we analyze the validity of the studied volatility stochastic models in describing the empirical IBOVESPA data.