Before revision:  In this paper, we show that the behaviors of price fluctuations in emerging cryptocurrency markets can be characterized fairly well by a Levy's stable distribution with alpha = 1.4 , which indicates fatter tails compared to a Gaussian distribution. Moreover, we have come to realize the limitations of the stable model especially under certain conditions outside time intervals ranging  from 30 minutes to 4 hours.
After revision:  In this paper, we show that the behaviors of price fluctuations in emerging cryptocurrency markets can be characterized fairly well by a Levy's stable distribution with alpha = 1.4 under certain conditions outside time intervals ranging from 30 minutes to 4 hours.