The Quantitative Finance Aspects of Automated Market Markers in DeFi

Paper: arXiv 2212.10974

Authors: Stefan Loesch

Abstract

Automated Market Makers (AMMs) are a class of smart contracts on Ethereum and other blockchains that “make markets” autonomously. In other words, AMMs stand ready to trade with other market participants that interact with them, at the conditions determined by the AMM. In this this paper, which relies on the existing and growing corpus of literature available, we review and present the key mathematical and quantitative finance aspects that underpin their operations, including the interesting relationship between AMMs and derivatives pricing and hedging.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical and mathematical synthesis of Automated Market Maker (AMM) mechanics and their deep connections to option pricing and impermanent loss hedging. However, as a review paper, it lacks original empirical data testing, robust backtesting frameworks, or statistical validation on real DeFi trade logs.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Quantitative & Math Aspects of AMMs in DeFi] --> B[Inputs: Existing DeFi Literature & Blockchain AMM Data]
    B --> C[Methodology: Mathematical Review & Theoretical Analysis]
    C --> D[Quantitative Modeling: AMM Mechanics, Derivatives Pricing & Hedging]
    D --> E[Key Finding: Structural Link Between AMM Dynamics & Options/Hedging]
    D --> F[Key Outcome: Comprehensive Quantitative Framework for AMM Operations]