Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach

The long-term dependence of Bitcoin (BTC), manifesting itself through a Hurst exponent $H>0.5$, is exploited in order to predict future BTC/USD price. A Monte Carlo simulation with ${10}^4$ geometric fractional Brownian motion realisations is performed as extensions of historical data. The accuracy of statistical inferences is 10%. The most probable Bitcoin price at the beginning of 2018 is 6358 USD.