Quantifying Arbitrage in Automated Market Makers: An Empirical Study of Ethereum ZK Rollups

Abstract

Arbitrage can arise from the simultaneous purchase and sale of the same asset in different markets in order to profit from a difference in its price. This work systematically reviews arbitrage opportunities between Automated Market Makers (AMMs) on Ethereum ZK rollups, and Centralised Exchanges (CEXs). First, we propose a theoretical framework to measure such arbitrage opportunities and derive a formula for the related Maximal Arbitrage Value (MAV) that accounts for both price divergences and liquidity available in the trading venues. Then, we empirically measure the historical MAV available between SyncSwap, an AMM on zkSync Era, and Binance, and investigate how quickly misalignments in price are corrected against explicit and implicit market costs. Overall, the cumulative MAV from July to September 2023 on the USDC-ETH SyncSwap pool amounts to $104.96k (0.24% of trading volume).