This paper conducts the first detailed analysis of the dynamics of Bitcoin prices. The application of a number of both linear and non-linear GARCH models indicates that the role of extreme price movements seems to be particularly pronounced: GARCH models with student-t innovations as well as combined jump-GARCH models are among the models with the best fit. This is reflected in both a relative increase in model performance and also compared to behavior of crude oil and gold prices. In contrast, no evidence of leverage effects is found. Market features such as the fixed supply of Bitcoin imply that Bitcoin is reminiscent of an exhaustible resource commodity. Whereas the supply of gold and oil are uncertain, there are no uncertainties on the Bitcoin supply-side. Thus, the observed price movements are attributable to demand side factors.