The rapid integration of digital asset markets, including cryptocurrencies, into the global and national economy demands new approaches to modeling and managing their unique risks. Traditional econometric and mathematical models based on the assumption of a normal probability distribution prove insufficient for describing the dynamics of highly volatile cryptocurrencies. This paper proposes a methodology for analyzing and managing investment risks under conditions of economic turbulence based on the theory of random processes with catastrophes and using Bitcoin as a case study. A combined model for the dynamics of the Bitcoin price logarithm is constructed, integrating a Wiener process (background dynamics) and a generalized Poisson process with negative jumps (catastrophic drops). An economic catastrophe concept is formalized as a daily return drop exceeding 8%. The model parameters (trend, volatility, intensity, and distribution of catastrophes) are estimated using the maximum likelihood method based on daily data from the 2020–2023 period. Analysis of historical data identified 23 catastrophic events with an average annual intensity of 5.75 and a mean drop magnitude of 11.8%. The model demonstrated high adequacy, revealing heavy-tailed risk distributions, the ability to obtain correct estimates of extreme risks, and the potential for constructing robust management systems. The obtained results expand the practical capabilities of risk management.
Glinsky et al. (Wed,) studied this question.