Comparing Bitcoin and Ethereum tail behavior via Q-Q analysis of cryptocurrency returns

ArXiv ID: 2507.01983 “View on arXiv”

Authors: A. H. Nzokem

Abstract

The cryptocurrency market presents both significant investment opportunities and higher risks relative to traditional financial assets. This study examines the tail behavior of daily returns for two leading cryptocurrencies, Bitcoin and Ethereum, using seven-parameter estimates from prior research, which applied the Generalized Tempered Stable (GTS) distribution. Quantile-quantile (Q-Q) plots against the Normal distribution reveal that both assets exhibit heavy-tailed return distributions. However, Ethereum consistently shows a greater frequency of extreme values than would be expected under its Bitcoin-modeled counterpart, indicating more pronounced tail risk.

Keywords: cryptocurrency, tail risk, heavy tails, Generalized Tempered Stable distribution, Bitcoin/Ethereum

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic calculus with the 7-parameter Generalized Tempered Stable distribution, including Lévy measures, characteristic exponents, and quantile estimation theorems, indicating high mathematical density. Empirical rigor is strong due to detailed parameter estimation with standard errors, goodness-of-fit tests, and specific data sourcing, though it lacks full backtest code or implementation details.

  flowchart TD
    A["Research Goal:<br>Compare Bitcoin & Ethereum Tail Risk"] --> B["Method: Q-Q Analysis<br>vs. Normal Distribution"]
    B --> C["Data Input:<br>Daily Returns"]
    C --> D["Computational Process:<br>Fit & Compare with<br>GTS-Distribution Parameters"]
    D --> E["Outcome 1:<br>Heavy Tails for Both"]
    D --> F["Outcome 2:<br>Ethereum Shows<br>More Extreme Values"]