Modelling the Volatility of the Price of Bitcoin

This study assessed the volatility and the Value at Risk (VaR) of daily returns of Bitcoins by conducting a comparative study in the forecast performance of symmetric and asymmetric GARCH models based on three different error distributions. The models employed are the SGARCH and TGARCH which were validated based on AIC, MAE and MSE measures. The results indicated that the SGARCH GED (1,1) with generalised error distribution term was identified as the best fitted GARCH model. Though, this best fitted model based on information loss (AIC) did not provide the best out-of-sample forecast, the differences was insignificant. Thus, the study clearly demonstrates that it is reliable to use the best fitted model for volatility forecasting. Also, to further validate the performance of the best fitted model, it was subjected to a historical back-test using Value at Risk (VaR). Though, it was evident from the study that no model was superior, it was indicated that an average loss of 1.2% is expected to be exceeded only 1% of the time. Moreover, volatility forecast from the back testing was relatively high during the first quarter of 2018 but begun decreasing steadily with time.