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

Arbitrage opportunities arise from the simultaneous buying and selling of the same asset in different markets to profit from price differences. This research systematically explores arbitrage possibilities between Automated Market Makers (AMMs) on Ethereum zk-roll-ups and Centralized Exchanges (CEXs). To start, we introduce a theoretical framework to assess arbitrage opportunities and develop a formula for the Maximal Arbitrage Value (MAV), considering both price discrepancies and the liquidity present in trading venues. Following this, we conduct an empirical assessment of the historical MAV between SyncSwap, an AMM on zkSync Era, and Binance, examining the speed at which price discrepancies are resolved considering both explicit and implicit market costs. Overall, the total MAV from July to September 2023 in the USDC-ETH SyncSwap pool amounts to $104.96K (0.24% of trading volume).