Two Models of Speculative Bubbles Dynamics for Cryptocurrency Prices

Abstract

The problem of investing into a cryptocurrency market requires good understanding of the processes that regulate the price of the currency. In this paper we offer a view of the cryptocurrency market as an environment for realization of self-organized speculative schemes that result in the formation of a characteristic price bubble. We use a microscale, agent-based model to simulate the system behavior and derive a macroscale ordinary differential equation (ODE) model to estimate the price and the return rates observed in the simulated agent-based model. We provide a formula for the total risk of the system expressed as a sum of two independent components, one being characteristic of the price bubble and the other of the investor behavior.