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This work is devoted to value-at-risk estimation using the copula method. The first part explores extreme value theory. We describe risk modeling and asset volatility. The second part presents a GJR-GARCH version of copulas to analyze asymmetric dependence, measuring complex non-linear relationships among stock index returns. We present a VAR measurement method based on extreme value theory and copula theory. The results show that copula-based methods are better at modeling dependence structure and yield better risk estimates.