Fees in AMMs: A quantitative study

ArXiv ID: 2406.12417 “View on arXiv”

Authors: Unknown

Abstract

In the ever evolving landscape of decentralized finance automated market makers (AMMs) play a key role: they provide a market place for trading assets in a decentralized manner. For so-called bluechip pairs, arbitrage activity provides a major part of the revenue generation of AMMs but also a major source of loss due to the so-called ‘informed orderflow’. Finding ways to minimize those losses while still keeping uninformed trading activity alive is a major problem in the field. In this paper we will investigate the mechanics of said arbitrage and try to understand how AMMs can maximize the revenue creation or in other words minimize the losses. To that end, we model the dynamics of arbitrage activity for a concrete implementation of a pool and study its sensitivity to the choice of fee aiming to maximize the revenue for the AMM. We identify dynamical fees that mimic the directionality of the price due to asymmetric fee choices as a promising avenue to mitigate losses to toxic flow. This work is based on and extends a recent article by some of the authors.

Keywords: Automated Market Maker (AMM), Arbitrage Dynamics, Toxic Flow, Dynamic Fees, Uniswap v4, Cryptocurrency/DeFi

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper utilizes advanced stochastic processes (random walks, geometric Brownian motion) and detailed analytical derivations, scoring high on math complexity. It also includes concrete simulation setups, sensitivity analyses, and references to implementation details for AMMs, demonstrating a strong empirical foundation for backtesting.

  flowchart TD
    A["Research Goal: Optimize AMM Fees<br/>to minimize losses from informed arbitrage"] --> B{"Key Methodology"}
    B --> C["Model Arbitrage Dynamics<br/>(e.g., based on Uniswap v4 mechanics)"]
    C --> D["Simulate sensitivity to<br/>various fee structures (static/dynamic)"]
    D --> E["Evaluate results:<br/>Maximize revenue / Minimize toxic flow loss"]
    E --> F["Key Findings & Outcomes"]
    F --> G["Dynamic Fees (directional/adaptive)<br/>significantly reduce losses<br/>while maintaining uninformed volume"]