Exponentially decayed double power-law distribution of Bitcoin trade sizes

Crypto Wash Trading

“…). Various studies on trading volumes or sizes have shown that the vast majority of tail exponents lie in the Pareto-Lévy regime ( < < ) for traditional financial assets and bitcoins (Li et al, 2019;Schnaubelt et al, 2019). 18 We thus check whether the values of exponent α in the fitted results fall within the Pareto-Lévy range.…”

“…Rounding could lead to violations of Benford's law for later digits, yet the first significant digits still follow Benford's law, as seen in multiple forensic applications (e.g.,Carslaw, 1988;Thomas, 1989). 17 For example, power-law distribution of tails can be found in Pareto distribution of income(Pareto, 1896), the distribution of stock returns(Gopikrishnan et al, 1999), trade size(Gopikrishnan et al, 2000), and share volume(Plerou et al, 2000), fluctuations in foreign exchange markets(Da Silva, Matsushita, Gleria, and Figueiredo, 2007;Ohnishi et al, 2008;Vandewalle, Ausloos, and Boveroux, 1997), and cryptocurrency transactions(Li et al, 2019;Schnaubelt et al, 2019)..…”

Are cryptos becoming alternative assets?

“…Second, we estimated the following parameters of the α-stable distribution, fitted to daily log-returns, to capture heavy tail behaviour: the tail exponent (Stable_α i,t ∈ (0, 2], with lower values indicating heavier tails) and the scale parameter (Stable_γ i,t ≥ 0). The α-stable distributions are a well-known class of distributions used in financial modeling (Rachev and Mittnik 2000), capturing the fat tails and the asymmetries of the realworld log-returns distributions (for their use in cryptocurrencies market, see Li et al 2019;Schnaubelt, Rende, and Krauss 2019;Muvunza 2020). The α-stable parameters were estimated using the empirical characteristic function method, following Koutrouvelis (1980Koutrouvelis ( , 1981 and Koutrouvelis and Bauer (1982).…”