A Stochastic Model for Cryptocurrencies in Illiquid Markets with Extreme Conditions and Structural Changes

Cryptocurrencies are increasingly utilized by investors and financial institutions worldwide. The current paper proposes a prediction model for a cryptocurrency that encompasses three properties observed in the markets for cryptocurrencies—namely high volatility, illiquidity, and regime shifts. By using Ito calculus, we provide a solution for the suggested stochastic differential equation (SDE) along with a proof. Moreover, numerical simulations are performed and are compared to the real data, which seems to capture the dynamics of the price path of a cryptocurrency in the real markets.