With the exception of Bitcoin, there appears to be little or no literature on GARCH modelling of cryptocurrencies. This paper provides the first GARCH modelling of the seven most popular cryptocurrencies. Twelve GARCH models are fitted to each cryptocurrency, and their fits are assessed in terms of five criteria. Conclusions are drawn on the best fitting models, forecasts and acceptability of value at risk estimates.

Bitcoin, the first electronic payment system, is becoming a popular currency. We provide a statistical analysis of the log-returns of the exchange rate of Bitcoin versus the United States Dollar. Fifteen of the most popular parametric distributions in finance are fitted to the log-returns. The generalized hyperbolic distribution is shown to give the best fit. Predictions are given for future values of the exchange rate.

We analyze statistical properties of the largest cryptocurrencies (determined by market capitalization), of which Bitcoin is the most prominent example. We characterize their exchange rates versus the U.S. Dollar by fitting parametric distributions to them. It is shown that returns are clearly non-normal, however, no single distribution fits well jointly to all the cryptocurrencies analysed. We find that for the most popular currencies, such as Bitcoin and Litecoin, the generalized hyperbolic distribution gives the best fit, while for the smaller cryptocurrencies the normal inverse Gaussian distribution, generalized t distribution, and Laplace distribution give good fits. The results are important for investment and risk management purposes.

Introduced in the 1980s, value at risk has been a popular measure of financial risk. However, value at risk suffers from a number of drawbacks as measure of financial risk. An alternative measure referred to as expected shortfall was introduced in late 1990s to circumvent these drawbacks. Much theory have been developed since then. The developments have been most intensive in recent years.However, we are not aware of any comprehensive review of known estimation methods for expected shortfall. We feel it is timely that such a review is written. This paper (containing six sections and over 140 references) attempts that task with emphasis on recent developments. We expect this review to serve as a source of reference and encourage further research with respect to measures of financial risk.