Optimal Routing in the Presence of Hooks: Three Case Studies

TL;DR

This paper explores optimal trade routing in networks of constant function market makers with hooks, enabling constraints and additional features like limit orders and noncomposable hooks, using convex optimization and dynamic programming.

Contribution

It introduces a unified framework for optimal routing with hooks, addressing three key case studies and providing practical solution methods.

Findings

Effective convex optimization formulations for routing with hooks.

Solutions for limit order routing, liquidations, and noncomposable hooks.

Practical algorithms for traders and liquidity providers.

Abstract

We consider the problem of optimally executing a user trade over networks of constant function market makers (CFMMs) in the presence of hooks. Hooks, introduced in an upcoming version of Uniswap, are auxiliary smart contracts that allow for extra information to be added to liquidity pools. This allows liquidity providers to enable constraints on trades, allowing CFMMs to read external data, such as volatility information, and implement additional features, such as onchain limit orders. We consider three important case studies for how to optimally route trades in the presence of hooks: 1) routing through limit orders, 2) optimal liquidations and time-weighted average market makers (TWAMMs), and 3) noncomposable hooks, which provide additional output in exchange for fill risk. Leveraging tools from convex optimization and dynamic programming, we propose simple methods for formulating and solving these problems that can be useful for practitioners.