Cryptocurrencies, Metcalfe's law and LPPL models

In this paper we investigate the statistical properties of cryptocurrencies by using alpha-stable distributions. We also study the benefits of the Metcalfe's law (the value of a network is proportional to the square of the number of connected users of the system) for the evaluation of cryptocurrencies. As the results showed a potential for herding behaviour, we used LPPL models to capture the behaviour of cryptocurrencies exchange rates during an endogenous bubble and to predict the most probable time of the regime switching.