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