Trading fees can offset losses for liquidity providers in continuous markets
Asymptotic Analysis of Trading Fees in CFMM
Cryptography and Security
Summary
Liquidity providers in decentralized finance pools earn fees when traders arbitrage price differences. This paper studies the amount of trading fees earned as the fee rate gets very small. The authors find a formula showing that fees from arbitrage fully cover losses caused by price movements when prices change continuously. They also show that only sudden jumps in price cause additional losses for liquidity providers beyond normal market risks.
What this means in practice
- •For defi protocol developers: Design trading fee structures that ensure liquidity providers recover losses in markets with smooth price changes.
- •For crypto traders: Estimate how arbitrage activity generates fees for liquidity providers and affects trading costs in slowly changing markets.
A theory result. No direct application yet.
Authors
Peiyang Jin, Clouds, Jing Qian
Abstract
As the dominant trading mechanism in decentralized finance, Automated Market Maker has been widely studied in research. However, limited research has been done with the trading fees taken into consideration. In this work, we study how much trading fee Liquidity Providers(LPs) can receive from arbitrage trading when the fee rate approaches zero. We give a closed-form formula for it and our result shows that the trading fees generated by arbitrage trading can fully offset the LVR loss when the price process is continuous. We further extend our conclusions to price processes with jumps and the theoretical analysis shows that jumps are the only cause of LP loss apart from market risks. Our results provide practical guidance for AMM designers as well as LPs.