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

Krzysztof Gogol, Johnnatan Messias, Deborah Miori, Claudio Tessone, Benjamin Livshits

TL;DR

This work systematically reviews arbitrage opportunities between Automated Market Makers on Ethereum ZK rollups, and Centralised Exchanges and derives a formula for the related Maximal Arbitrage Value (MAV) that accounts for both price divergences and liquidity available in the trading venues.

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).

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

TL;DR

This work systematically reviews arbitrage opportunities between Automated Market Makers on Ethereum ZK rollups, and Centralised Exchanges and derives a formula for the related Maximal Arbitrage Value (MAV) that accounts for both price divergences and liquidity available in the trading venues.

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).
Paper Structure (24 sections, 18 equations, 6 figures)

This paper contains 24 sections, 18 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Background: Rollups, DEXs and CEXs
  3. Layer-2 and Rollups
  4. Crypto Centralised Exchanges
  5. Decentralised Exchanges
  6. Automated Market Makers.
  7. Constant Product Market Makers (CPMM).
  8. CPMM with Concentrated Liquidity (CLMM).
  9. The Theory of Arbitrage on AMMs
  10. Maximal Arbitrage Value
  11. Arbitrage between a CPMM and CEX.
  12. Empirical Case Study: zkSync Era
  13. Dataset We Used
  14. Proposed Analysis Framework
  15. Empirical MAV from the USDC-ETH Pool
  16. ...and 9 more sections

Figures (6)

  • Figure 1: Architecture of a rollup.
  • Figure 2: Explanatory plots for the price differences for USDC-ETH among SyncSwap AMM on zkSync Era and Binance. The AMM spot price oscillates around the CEX price and we can notice how misalignments expand and then decay over several minutes.
  • Figure 3: Empirical MAV, price misalignment and reserves in the USDC-ETH pool at SyncSwap on zkSync Era.
  • Figure 4: We cluster our data points relating to MAV events. The inertia plot suggests an optimal clustering into $5$ groups, which are visualised via a t-SNE projection and analysed in the proposed table.
  • Figure 5: OLS model for the prediction of time of decay of price misalignments. Features have been standardised but not de-meaned.
  • ...and 1 more figures