Statistical properties of exchange rates of cryptocurrencies and their market dynamics as compared to selected fiat currencies

The development of cryptocurrencies was the consequence of the endeavours of some circles of computer scientists associated with anarchist views to create a medium of exchange that would be decentralised, independent from institutions creating monetary policy, governments and politicians, and whose functioning would not require any clearing institutions. The first cryptocurrency that fulfilled most of these postulates was Bitcoin. In a relatively short time, it became very popular among investors and reached a significant capitalisation on financial markets, but soon became an object of speculation rather than a medium of exchange. So far, no common view has been established as to whether Bitcoin is closer to being money, an object of speculation or an investment asset. The question what Bitcoin really is has fundamental importance not only to the entire cryptocurrency project, but also to the economy in general.
The purpose of the study discussed in the article was to compare the statistical properties of cryptocurrency exchange rates (on the example of Bitcoin) with such properties of the exchange rates of fiat currencies, and to assess whether investments on the Bitcoin market can be considered similar to investments on fiat currency markets in terms of some analysed features. Basic statistical characteristics of the relative increments in the exchange rates of Bitcoin and four fiat currencies paired with the US dollar were analysed, as were some selected properties of stochastic processes that could be used to model the dynamics of those increments. In addition, a theoretical analysis of both Bitcoin and some other cryptoassets was carried out, which explained, among other things, why the study compared Bitcoin with currencies and not with investment assets.
The research demonstrated that there are differences between several statistical properties of Bitcoin and those of fiat currencies. In addition to the generally higher unconditional volatility, differences were observed between the trends in exchange rates of Bitcoin and fiat currencies versus the US dollar, the levels of relative increments in the exchange rates, the conditional volatility, and the residual distributions.

