The objective of this paper is to determine the basic features of the use of mathematical modeling of the system to forecast cryptocurrency exchange rate. The study determines that cryptocurrency is the simplest investment asset being and, at the same time, the riskiest one. Advantages and disadvantages of cryptocurrency use are specified. Advantages include: code openness, anonymity, decentralization, emission, and reliability. Disadvantages include lack of guarantees, instability, risk of prohibition and possible loss. A model to forecast bitcoin cryptocurrency exchange rate is proposed and substantiated mathematically. The observations are the basis to develop a hypothesis: the faster the cryptocurrency (e.g. bitcoin) is mined, the more difficult it is to forecast bitcoin cryptocurrency exchange rate. Certain factors emphasize which may affect the cryptocurrency exchange rate: trade wars of the USA with other export-oriented world economies (China); advent of IEO as the alternative for ICO and new drivers connected with the interest in cryptocurrency; FATF recommendations for market control, the entry of world giants (e.g. Facebook) into the crypto-market and the development of the stablecoin market.