Bitcoin (BTC/USD) price is modeled as a stochastic process following a fractional Brownian motion (fBm) demonstrated via a Hurst exponent (H) to try and measure the long term memory in the time series. Monte Carlo simulations were performed on this model to extend historical data and forecast Bitcoin price. Out of sample simulation results showed accuracy was to within ~10% of current prices. The 180 day (6 month) most probable (median) forward looking Bitcoin price prediction is ~USD14,211 by May 2018 and implying upside risk of ~95%. In addition, within this time frame Quantile risk/loss estimates show that there is only a 5% tail-end risk of a drop back to the ~$2000 price level (or a ~70% price drop).