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Automated Market Making and Arbitrage Profits in the Presence of Fees

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arxiv 2305.14604 v2 pith:246BNPQE submitted 2023-05-24 q-fin.MF math.OCq-fin.PMq-fin.PRq-fin.TR

Jason Milionis , Ciamac C. Moallemi , Tim Roughgarden This is my paper · ORCID
classification q-fin.MFmath.OCq-fin.PMq-fin.PRq-fin.TR
keywords feesarbitrageblockmodelprofitstradingarbitrageursasymptotic
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We consider the impact of trading fees on the profits of arbitrageurs trading against an automated market maker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers (LPs) due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to introduce both fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of blocks which present profitable trading opportunities to arbitrageurs. This fraction decreases with an increasing block rate, hence our model yields an important practical insight: faster blockchains will result in reduced LP losses. Further introducing gas fees (fixed costs) in our model, we show that, in the fast block asymptotic regime, lower gas fees lead to smaller losses for LPs.

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Cited by 6 Pith papers

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