Purpose: The purpose of this thesis is to investigate and assess the predictive ability of the GARCH (1,1), IGARCH (1,1), EGARCH (1,1), GJR-GARCH (1,1), APARCH (1,1), TGARCH (1,1) and CGARCH (1,1) models in forecasting the volatilities of six major cryptocurrencies: Bitcoin, Ripple, Litecoin, Monero, Dash, Dogecoin and six world currencies: Euro, British Pound, Canadian Dollar, Australian Dollar, Swiss Franc and the Japanese Yen. The optimal volatility model selected for each virtual and hard currency is then integrated into the Volatility Update Historical Simulation approach to evaluate the ...