CFMM中交易费用的渐近分析
Asymptotic Analysis of Trading Fees in CFMM
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中文总结 AI 辅助
本文研究CFMM中费率趋近零时LP从套利交易中获得的交易费用，给出闭式公式，证明连续价格下费用可完全抵消LVR损失，跳跃是唯一额外损失来源，为AMM设计提供指导。
中文摘要 AI 辅助
作为去中心化金融中的主导交易机制，自动做市商（AMM）已被广泛研究。然而，考虑交易费用的研究却十分有限。在本工作中，我们研究了当费率趋近于零时，流动性提供者（LPs）能从套利交易中获得多少交易费用。我们给出了其闭式公式，结果表明，当价格过程连续时，套利交易产生的交易费用可以完全抵消LVR损失。我们进一步将结论扩展到具有跳跃的价格过程，理论分析表明，跳跃是除市场风险外LP损失的唯一原因。我们的研究结果为AMM设计者以及LPs提供了实践指导。
英文摘要
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.
