Fees in AMMs: A quantitative study

Paper: arXiv 2406.12417

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (36)

1. Automated Market Making and Loss-Versus-Rebalancing (2022) — link
2. An Economic Model of a Decentralized Exchange with Concentrated Liquidity (2023)
3. Automated Market Making and Arbitrage Profits in the Presence of Fees — → 2305.14604
4. Automated Market Makers: A Practical Guide to Decentralized Exchanges and Cryptocurrency Trading (2023) — link
5. A theoretical framework for dynamical fee choice in AMMs (2024) — link
6. Theory and Practice of Revenue Management (2005)
7. Decentralized exchanges (2021)
8. The adoption of blockchain-based decentralized exchanges (2021) — link

2 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.