Using Uniswap v3 Liquidity Positions to Approximate Other AMMs
Summary
The document explains how Uniswap v3’s range-based liquidity positions can be arranged to approximate the liquidity behavior of other two-asset automated market makers. It represents an AMM’s local liquidity across logarithmic price ticks as a curve, calling the resulting shape a liquidity fingerprint. Narrower, more numerous positions can more closely reproduce a target curve, while the local liquidity measure captures how reserves respond to price changes.
Examples connect a flat liquidity profile to Uniswap v2’s constant-product pool, a bounded position to a constant-parameter Curve StableSwap case, an exponential profile to weighted Balancer pools, and a hyperbolic-secant profile to the logarithmic market scoring rule. These comparisons provide a conceptual derivation method, rather than a tested implementation. The analysis assumes continuously divisible tick space and focuses on two assets; real ticks are discrete, position updates consume gas, and some AMMs may not translate readily into a liquidity function. The document leaves practical numerical approximation and gas-efficient implementation for future work.
Key ideas
- A Uniswap v3 position supplies liquidity only within its selected price interval.
- A sequence of positions can approximate the price-dependent liquidity profile of another AMM.
- The shape of liquidity across logarithmic price ticks provides a fingerprint of an AMM’s reserve curve.
- The document relates distinct profile shapes to constant-product, stable-swap, weighted-pool, and LMSR designs.
- Discrete ticks, gas costs, and curve representation limit practical replication.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.