The main purpose of the thesis is comparing the results of volatility estimation under different models and observation frequencies. These models include GARCH, EGARCH and TGARCH models. Both testing for the goodness-of-fit and sample forecasting will be conducting in the thesis. Empirical results show that higher observation frequency stands for higher goodness-of-fit when estimating in foreign exchange volatility. Another implication from the research is that both EGARCH and TGARCH model generally position higher goodness-of-fit than GARCH model.