A theoretical framework for fees in AMMs

ArXiv ID: 2404.03976 “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 value retention. We manage to map the ensuing dynamics to that of a random walk with a specific reward scheme that provides a convenient starting point for further studies.

Keywords: Automated Market Makers (AMMs), Arbitrage Mechanics, Fee Optimization, Random Walk, Value Retention, DeFi (Decentralized Finance)

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic modeling and calculus to map AMM arbitrage dynamics to random walks, indicating high math complexity. However, it relies entirely on theoretical simulations and synthetic data without backtesting or real-world datasets, resulting in low empirical rigor.

  flowchart TD
    A["Research Goal: Determine optimal AMM fees<br>to maximize value retention"] --> B{"Methodology"};
    B --> C["Model Arbitrage Dynamics<br>for Concrete AMM Implementation"];
    C --> D["Simulate Activity & Analyze<br>Sensitivity to Fee Parameter"];
    D --> E["Map Dynamics to<br>Random Walk with Reward Scheme"];
    E --> F["Key Finding: Fee Optimization<br>Directly Impacts Value Retention"];
    F --> G["Outcome: Theoretical Framework<br>for Future AMM Design"]