On protocol robustness and extreme tail risk: Fréchet vs. Gumbel domains across cryptocurrencies and traditional assets, 2022-2024

Luis-Felipe Arizmendi ()
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Luis-Felipe Arizmendi: Comillas Pontifical University

Economics Bulletin, 2026, vol. 46, issue 3, 1094 - 1099

Abstract: This paper applies Generalized Extreme Value (GEV) theory to identify the distributional tail domain of daily losses across a seven-asset portfolio—three cryptocurrencies (Bitcoin, Ethereum, Solana), two G10 currency pairs (EUR/USD, CAD/USD), an emerging-market currency (MXN/USD), and Gold—over N = 757 synchronized trading days spanning January 2022 to November 2024. Block-maxima estimation over 36 monthly blocks yields GEV shape parameters ? consistently above zero for all three cryptocurrencies (BTC: 0.171; ETH:0.281; SOL: 0.310), placing their loss distributions in the Fréchet (heavy-tail) domain; AIC confirms the GEV specification over the Gumbel for Ethereum and Solana. Traditional assets are consistent with the lighter-tailed Gumbel domain. The Normal distribution systematically understates the empirical 99% Value at Risk of cryptocurrencies by up to 2.45 percentage points, while closely approximating VaR for all currency and Gold positions. A Chow structural break test applied to the AR(1) mean equation detects crypto-specific mean instability at the FTX exchange collapse (November 2022)—not transmitted to currency or commodity markets—while the 2024 U.S. electoral cycle produces no structural break in any of the seven assets. These findings carry direct implications for EVT-based capital adequacy frameworks for digital asset portfolios.

Keywords: Crypto-tokens economics; Extreme Value Theory; tail risk; protocol robustness; Gumbel distribution (search for similar items in EconPapers)
JEL-codes: E5 G1 (search for similar items in EconPapers)
Date: 2026-09-30
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