This paper investigates the implementation of asymmetric models and skewed distributions when managing market risk using the Value-at-Risk. The comparative analysis of the VaR estimations is executed by consideration of the time dynamics and the sequence of potential violation of the model. The findings of the paper suggest that the consideration of skewed distributions of time series and asymmetric volatility specification result to more accurate estimations of the VaR and hence provide the means for more efficient estimators of the potential losses that an institution is likely to exhibit. The importance of the paper lies on the fact that according to the regulative authorities financial institutions are supposed to adopt internally models for managing more efficiently market risk and this could be achieved by applying asymmetric models on both the volatility of their assets and on the distributions of the examined time series.