A Monte Carlo Approach to Bitcoin Price Prediction with Fractional Ornstein–Uhlenbeck Lévy Process

Since its inception in 2009, Bitcoin has increasingly gained main stream attention from the general population to institutional investors. Several models, GARCH type jump-diffusion type, have been developed dynamically capture price movement of this highly volatile asset. While fitting Gaussian and Generalized Hyperbolic Normal Inverse (NIG) distributions log-returns Bitcoin, NIG distribution appears provide best fit. The time-varying Hurst parameter for reveals periods randomness mean-reverting behaviour, motivating study paper through fractional Ornstein–Uhlenbeck driven by a Lévy process. Features such as long-range memory are jump diffusion processes that well captured with model. results present 95% prediction some specific dates. This contributes literature forecasts useful options traders.