Stability and Fractality in the Behavior of Currencies: Comparing Crypto Versus National Currencies

Abstract

The current debate over adopting cryptocurrencies as legal tender, even as a replacement for fiat currencies, requires an analysis of the properties of different types of money. In this paper, we examine various statistical parameters characterizing the evolution of a sample of both national currencies and cryptocurrencies. Our goal is to identify any differences in their behaviors. This analysis is relevant for assessing the advantages and disadvantages of adopting cryptocurrencies as legal tender. We find that all the currencies follow self-similar processes while regulated ones are allstable, in terms of their Lyapunov coefficients. In turn, some cryptocurrencies have a sensitive dependence on initial conditions. We also find that regulated currencies, including the so-called stablecoins, tend to exhibit less concentrated distributions of their idiosyncratic parameters, particularly the Hurst and the Lyapunov exponents.