When we need to develop an estimation of Market VaR, we must predict the probability of a maximum loss. To comply with this objective we must predict the volatility for the next period and the probability associated with this value.
This paper contains a development of Garch theory and the application of different, symmetric and asymmetric models, to predict the volatility of financial series, accompanied with the theory of Extreme Value Theory, EVT, and others heavy tails distributions to estimate the probability that the maximum loss may be occurred.
In the first part I analyze the presence of different Garch models in the returns of stocks in several markets and compare the same with other models in use. In the second part it is presented the estimation of the probability associated with the volatility forecasted. The methods used are the Kupiec estimation of the probability the Extreme Value Theory, and other heavy tails distributions as Weibull, Pareto, Pearson, etc. In the third part there are an estimation of several methods, for different series of returns. In the fourth part there are presented the results and the different methods used. Finally in the last part there are the conclusions arrived
Keywords: Arch, Garch, Egarch, Tarch, EVT (Extreme Value Theory) Kupiec, Pareto, Heteroscedasticity, VaR (Value at Risk), Market Risk, Kolmogorov Smirnov Test, Anderson Darling Test, Basel II
