Triangular Pricing Consistency and Limits to Arbitrage in Ethereum Markets

Abstract

Abstract Cross-numeraire pricing efficiency is central in digital asset markets because the same asset trades continuously against fiat, Bitcoin, and stablecoin-linked numeraires. This paper studies Ethereum (ETH) triangular consistency across ETH/USD, ETH/BTC, and BTC/USD prices, where USD denotes the U.S. dollar and BTC denotes Bitcoin. The benchmark requires the direct ETH/USD price to equal the synthetic price implied by ETH/BTC and BTC/USD. Using single-venue Coinbase true-USD hourly data from January 2022 through June 2023, I find that the log wedge has a near-zero mean, Augmented Dickey-Fuller diagnostics reject a unit root, first-order persistence is low, and absolute wedges widen during stress episodes. A Binance extension using Tether (USDT) as the dollar proxy shows a tighter unconditional wedge, which cautions against treating stablecoin denomination as the dominant average source of deviations in this sample. A Gate.io order-book extension for the Terra/Luna, FTX, and USD Coin-Silicon Valley Bank (USDC-SVB) stress windows constructs bid-ask executable bands and finds no positive after-fee executable breach across 524 common event-hour observations. The results show that Ethereum cross-numeraire prices are tightly consistent on average, but stress-state wedges should be interpreted as frictional parity deviations rather than executable arbitrage opportunities. JEL Classification: G12 , G14 , G15 , G23 , C58