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In this paper, we show some results regarding the evaluation of Value-at-Risk (VaR) of some portfolios using a Gaussian Copula, modified by introducing the Generalized Correlation Coefficient, and assuming a Generalized Error Distribution (G.E.D.) for the single returns in the portfolios. In the literature, various authors considered the Copula function approach to evaluate market risk. In our proposal we consider a Lp_min algorithm to estimate p, the shape parameter of the distribution. Finally, we compare the classical RiskMetrics method with our G.E.D. method based on a modified Gaussian Copula.