Since the 90 decade, the use of Value at Risk (VaR) methodology has been disseminated among both financial and non-financial institutions around the world, as a good practice in terms of risks management. The existence of fat tails is one of the striking stylized facts of financial returns distributions. This fact makes the use of traditional parametric models for Value at Risk (VaR) estimation unsuitable for the estimation of low probability events. This is because traditional models are based on the conditional normality assumption for financial returns distributions. The main purpose of this dissertation is to investigate the performance of VaR models based on Extreme Value Theory. The results indicates that Extreme Value Theory based models are suitable for low probability VaR estimation.