Automated Market Making and Arbitrage Profits in the Presence of Fees

Ciamac Moallemi

Trading fees and discrete block generation affect the maximal extracted value (MEV) generated by arbitrageurs trading against an automated marker marker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers (LPs) due to DEX-CEX arbitrage. Ciamac Moallemi (Columbia) starts by reintroducing the idea of “loss-versus-rebalancing” (LVR), which quantifies the loss to arbitrageurs in an idealized, continuous-time setting with no trading fees. Trading fees and discrete blocks, however, create frictions which impact arbitrage activity.

Ciamac presents a formula that simplifies when the trading fee is low and blocks are frequent (the “fast block” regime). In this case arbitrage profits are simply LVR scaled down by the probability of an arbitrage trade in any given block. Moreover, although LVR was developed assuming no fees and continuous trading, with fees and discrete blocks, LVR is roughly the profit gross of fees of arbing the pool. Introducing fees simply changes how LVR is split and who earns it (arbitrageurs or pool LPs).

Arbitrage MEV scales with the square root of the interblock time, which suggests that faster blockchains are one mechanism to reduce arbitrage MEV. Trading fees also create a trade-off between losses to arbitrageurs and larger effective spreads for all traders. The model quantifies this trade-off and provides a path toward setting revenue optimal fees.

This is joint work with Jason Milionis and Tim Roughgarden.

About the speaker

Ciamac is the William von Mueffling Professor of Business in the Decision, Risk, and Operations Division of the Graduate School of Business at Columbia University. A high school dropout, he received undergraduate degrees in EECS and Mathematics from MIT. As a Marshall Scholar, he completed Part III of the Mathematical Tripos at Cambridge. He received a doctorate in EE from Stanford. Prior to his doctoral studies, he developed quantitative methods in a number of entrepreneurial ventures. He also develops quantitative trading strategies at Bourbaki LLC, a quantitative investment advisor. His research interests are in the development of mathematical and computational tools for optimal decision making under uncertainty, with a focus on applications areas including market microstructure, and quantitative and algorithmic trading. He has done past work in the core economics of blockchain technology (transaction fee mechanisms), and is also interested in applications in decentralized finance. More:

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