DeFi's Concentrated Liquidity From Scratch

TL;DR

This paper provides a comprehensive theoretical and geometric analysis of concentrated liquidity mechanisms in DeFi, synthesizing existing descriptions and extending them with trigonometric insights to deepen understanding of decentralized exchange infrastructure.

Contribution

It offers an organized, algebraic, and geometric elaboration of concentrated liquidity models from key DeFi protocols, creating an authoritative overview of their underlying theory.

Findings

Unified framework for liquidity descriptions

Geometric interpretation of liquidity concentration

Enhanced understanding of DeFi exchange mechanics

Abstract

The scope of this article includes the three preeminent descriptions of concentrated liquidity from Bancor (2020 and 2022), and Uniswap (2021), as well as three additional descriptions informed by trigonometric analysis of the same. The purpose of this contribution is to organize the seminal and derivative forms of this cornerstone DeFi technology, and algebraically and geometrically elaborate these descriptions to achieve an authoritative and near-exhaustive overview of the underlying theory powering the current state-of-the-art in decentralized exchange infrastructure. This material was created for the Token Engineering Academy Study Season 2024, a cohort-based online program scheduled for April-July 2024. The Study Season offers access to a bachelor-level online learning program, and complementary live tracks with the most influential practitioners and researchers in the sector - all provided as free, public goods.