Characteristics of price related fluctuations in Non-Fungible Token (NFT) market

TL;DR

The present work studies capitalization, floor price, the number of transactions, the inter-transaction times, and the transaction volume value of a few selected popular token collections to conclude that the NFT market, although young and governed by somewhat different mechanisms of trading-shares several statistical properties with the regular financial markets.

Abstract

A non-fungible token (NFT) market is a new trading invention based on the blockchain technology which parallels the cryptocurrency market. In the present work we study capitalization, floor price, the number of transactions, the inter-transaction times, and the transaction volume value of a few selected popular token collections. The results show that the fluctuations of all these quantities are characterized by heavy-tailed probability distribution functions, in most cases well described by the stretched exponentials, with a trace of power-law scaling at times, long-range memory, and in several cases even the fractal organization of fluctuations, mostly restricted to the larger fluctuations, however. We conclude that the NFT market - even though young and governed by a somewhat different mechanisms of trading - shares several statistical properties with the regular financial markets. However, some differences are visible in the specific quantitative indicators.

Figures (6)

• Figure 1: Collection characteristics: (a) total capitalization $C$ expressed in SOL and USD, (b) transaction volume value $V_{\Delta t}$ in SOL and in USD, (c) floor price $p_{\rm fl}$ in SOL and in USD, (d) transaction number aggregated hourly $N_{\Delta t}$ for all 5 collections: Blocksmith Labs Smthys (BM), Famous Fox Federation (FF), Lifinity Flares (LF), Okay Bears (OKB), and Solana Monkey Business (SM).
• Figure 2: (a) Probability distribution functions for absolute values of logarithmic increments of collection capitalization expressed in solana $|c_{\Delta t}^{^{\rm SOL}}|$ (top left) and US dollar $|c_{\Delta t}^{^{\rm USD}}|$ (top right), the number of transactions aggregated hourly $N_{\Delta t}$ (bottom left), and inter-transaction times $\delta t$ (bottom right). (b) Probability distribution functions for absolute values of floor price returns expressed in SOL $|r_{\Delta t}^{^{\rm SOL}}|$ (top left) and USD $|r_{\Delta t}^{^{\rm USD}}|$ (top right) and volume value expressed in solana $V_{\Delta t}^{^{\rm SOL}}$ (bottom left) and US dollar $V_{\Delta t}^{^{\rm USD}}$ (bottom right). The appropriate power law (long-dashed) and stretched-exponential (short-dashed) models are also shown as guides for an eye together with their parameter values $\gamma$ and $\beta$, respectively.
• Figure 3: (a) Autocorrelation function for absolute values of logarithmic increments of collection capitalization expressed in solana $|c_{\Delta t}^{^{\rm SOL}}|$ (top left) and US dollar $|c_{\Delta t}^{^{\rm USD}}|$ (top right), the number of transactions aggregated hourly $N_{\Delta t}$ (bottom left), and inter-transaction times $\delta t$ (bottom right). (b) Autocorrelation function for absolute values of floor price returns expressed in SOL $|r_{\Delta t}^{^{\rm SOL}}|$ (top left) and USD $|r_{\Delta t}^{^{\rm USD}}|$ (top right) and volume value expressed in solana $V_{\Delta t}^{^{\rm SOL}}$ (bottom left) and US dollar $V_{\Delta t}^{^{\rm USD}}$ (bottom right).
• Figure 4: Multifractal analysis of time series representing three NFT collections: (a) FF, (b) LF, and (c) OKB. The respective fluctuation functions $F_q(s)$ with $-4 \leqslant q \leqslant 4$ were calculated for the logarithmic increments of collection capitalization expressed in solana $c_{\Delta t}^{^{\rm SOL}}$ and US dollar $c_{\Delta t}^{^{\rm USD}}$ and floor price returns expressed in the same currencies: $r_{\Delta t}^{^{\rm SOL}}$ and $r_{\Delta t}^{^{\rm USD}}$. A range of scales, in which a power-law form of $F_q(s)$ is observed for a range of values of $q$, is denoted by vertical red dashed lines on each plot. The heavy green lines in each panel correspond to $F_q(s)$ with $q=2$ and serve calculation of the Hurst exponents $H$ (the range-of-scales restrictions do not apply here).
• Figure 5: The same as in Fig. \ref{['fig::Fq.1']} but for different quantities: the number of transactions aggregated hourly $N_{\Delta t}$, inter-transaction times $\delta t$, and transaction volume value aggregated hourly expressed in solana $V_{\Delta t}^{^{\rm SOL}}$ and US dollar $V_{\Delta t}^{^{\rm USD}}$. The heavy green lines in each panel correspond to $F_q(s)$ with $q=2$ and serve calculation of the Hurst exponents $H$ (the range-of-scales restrictions do not apply here).