A Microstructure Analysis of Coupling in CFMMs

ArXiv ID: 2510.06095 “View on arXiv”

Authors: Althea Sterrett, Austin Adams

Abstract

The programmable and composable nature of smart contract protocols has enabled the emergence of novel market structures and asset classes that are architecturally frictional to implement in traditional financial paradigms. This fluidity has produced an understudied class of market dynamics, particularly in coupled markets where one market serves as an oracle for the other. In such market structures, purchases or liquidations through the intermediate asset create coupled price action between the intermediate and final assets; leading to basket inflation or deflation when denominated in the riskless asset. This paper examines the microstructure of this inflationary dynamic given two constant function market makers (CFMMs) as the intermediate market structures; attempting to quantify their contributions to the former relative to familiar pool metrics such as price drift, trade size, and market depth. Further, a concrete case study is developed, where both markets are constant product markets. The intention is to shed light on the market design process within such coupled environments.

Keywords: Constant function market makers, CFMMs, Smart contracts, DeFi market microstructure, Price inflation, Cryptocurrency/DeFi

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper uses advanced calculus and differential equations to model price drift and marginal swap depth in coupled CFMMs, demonstrating high mathematical density. However, it is purely theoretical with no backtests, datasets, or empirical implementation details, focusing on analytical derivations rather than real-world data.
  flowchart TD
    A["Research Goal:<br>Quantify CFMM Coupling<br>Microstructure & Inflation"] --> B["Methodology:<br>Analytical Modeling &<br>Case Study (Constant Product)"]
    B --> C["Inputs/Assumptions:<br>Two Coupled CFMMs (xy=k),<br>Trade Flows, Liquidity Pools"]
    C --> D["Computational Process:<br>Derive Price Impact &<br>Basket Inflation Mechanics"]
    D --> E["Key Outcomes:<br>1. Links Price Drift/Depth to Inflation<br>2. Confirms Architectural Friction<br>3. Informs Market Design"]