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This dissertation focuses on the estimation of Value at Risk in six European Stock Exchanges from the beginning of the millennium. It presents the theoretical framework regarding the VaR techniques as well as the ARCH models which are commonly used in the estimation of market risk. On the empirical part, the dissertation provides an insight into parametric models like Risk Metrics and non parametric like Historical Simulation and in order to evaluate their predictive ability during the recent global financial crisis they are backtested. In addition, models of the ARCH family are being presented extensively since they are commonly used in the VaR forecasting procedure. The Akaike’s Information as well as the Schwarz’s Bayesian Information Criterion are examined so as to be concluded if the aforementioned models are trustworthy and could predict VaR accurately.