This paper provides a thorough overview and further clarification surrounding the volatility behavior of the major six cryptocurrencies (Bitcoin, Ripple, Litecoin, Monero, Dash and Dogecoin) with respect to world currencies (Euro, British Pound, Canadian Dollar, Australian Dollar, Swiss Franc and the Japanese Yen), the relative performance of diverse GARCH-type specifications namely the SGARCH, IGARCH (1,1), EGARCH (1,1), GJR-GARCH (1,1), APARCH (1,1), TGARCH (1,1) and CGARCH (1,1), and the forecasting performance of the Value at Risk measure. The sampled period extends from October 13th 2015 till November 18th 2019. The findings evidenced the superiority of the IGARCH model, in both the in-sample and the out-of-sample contexts, when it deals with forecasting the volatility of world currencies, namely the British Pound, Canadian Dollar, Australian Dollar, Swiss Franc and the Japanese Yen. The CGARCH alternative modeled the Euro almost perfectly during both periods. Advanced GARCH models better depicted asymmetries in cryptocurrencies' volatility and revealed persistence and "intensifying" levels in their volatility. The IGARCH was the best performing model for Monero. As for the remaining cryptocurrencies, the GJR-GARCH model proved to be superior during the in-sample period while the CGARCH and TGARCH specifications were the optimal ones in the out-of-sample interval. The VaR forecasting performance is enhanced with the use of the asymmetric GARCH models. The VaR results provided a very accurate measure in determining the level of downside risk exposing the selected exchange currencies at all confidence levels. However, the outcomes were far from being uniform for the selected cryptocurrencies: convincing for Dash and Dogcoin, acceptable for Litecoin and Monero and unconvincing for Bitcoin and Ripple, where the (optimal) model was not rejected only at the 99% confidence level.