Automated Market Making and Arbitrage Profits in the Presence of Fees

ArXiv ID: 2305.14604 “View on arXiv”

Authors: Unknown

Abstract

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.

Keywords: automated market maker (AMM), arbitrage, liquidity provision, blockchain, Crypto/DeFi

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper relies heavily on advanced stochastic calculus, Markov jump-diffusion processes, and asymptotic analysis to derive closed-form expressions, indicating high mathematical complexity. However, it lacks empirical backtesting, datasets, or statistical performance metrics, focusing instead on theoretical modeling and asymptotic insights.

  flowchart TD
    A["Research Goal: Model impact of trading fees & gas<br>on AMM arbitrage profits/LP losses"] --> B["Methodology: Extend Milionis et al. model<br>with fees & discrete Poisson block times"]
    B --> C["Data/Inputs: General two-asset AMM<br>fee rate, block generation rate, gas fees"]
    C --> D["Computation: Derive closed-form expression<br>for expected instantaneous arbitrage profit"]
    D --> E{"Asymptotic Analysis: Fast block regime"}
    E --> F["Key Finding: Fees scale profits by fraction<br>of profitable blocks; this fraction ↓ with ↑ block rate"]
    E --> G["Key Finding: Faster blockchains reduce LP losses<br>Lower gas fees further reduce losses"]