A Tick-by-Tick Solution for Concentrated Liquidity Provisioning

Paper: arXiv 2405.18728

Abstract

Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision of liquidity at each tick under a given set of parameter estimates for swap volume and price volatility. Surprisingly, early results show that concentrating liquidity around the current price is usually not the best strategy.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced convex optimization and water-filling algorithms, but lacks backtest results, statistical metrics, or production-ready implementation details, focusing instead on theoretical problem formulation.

Research Flowchart

  flowchart TD
  A["Research Goal: Maximize fees & reserves<br>in CLMM liquidity provision"] --> B["Model as<br>Convex Optimization Problem"]
  B --> C["Inputs: Swap Volume &<br>Price Volatility Estimates"]
  C --> D["Compute: Optimal Tick-by-Tick<br>Liquidity Distribution"]
  D --> E["Outcome 1: Liquidity is<br>not best concentrated at current price"]
  D --> F["Outcome 2: Programmable tick-level<br>solution for fee maximization"]