Concentrated Liquidity

Introduction

Liquidity in classic AMM is distributed uniformly in the entire price range from 0 to infinity.

We can improve capital efficiency, especially for certain pairs where you can expect trades to occur within a tight range. Take USDC/USDT for example, where most trading happens between $0.99 and $1.01. In this case, liquidity outside of this range is largely untouched and would be better off used elsewhere.

With the Liquidity Book (LB), liquidity providers can instead provide liquidity within a specified price range of their choice - this is called concentrated liquidity. Using the USDC/USDT pair as an example again, if an LP chooses to provide liquidity between $0.99 and $1.01 then the LP will earn trading fees so long price is within that range.

Bin Pricing

Liquidity Book allows liquidity to be distributed across discrete bins with fixed width. Liquidity can be exchanged at fixed price within each bin. Each bin represents a single price point and the difference between two consecutive bins is the bin step. Take for example USDC/USDT again. If the current price is $1 and the bin step is 1 basis point (i.e. 0.0001 or 0.01%), then the next consecutive bins up are 1 ∗ 1.0001 = $ 1.0001 1∗1.0001=$1.0001, 1.0001 ∗ 1.0001 = $ 1.00020001 1.0001∗1.0001=$1.00020001, etc. Note that this is the geometric sequence $1.0001^n$.

Bin steps are configurable parameters set by the pool creator. There can be multiple markets of the same pair but varying only in their bin step. Liquidity pools in Liquidity Book are uniquely identified by its tuple $(X,Y,s)$of pooled assets $X, Y$and bin step $s$.

Liquidity Book vs Uniswap V3

• Uniswap V3 concentrate liquidity within a fixed bound with continuous $X * Y = k$ curve.

• Liquidity Book discretizes liquidity into fixed width bins, with fixed price $X + Y = k$ within each bin.

• TLDR; Uni-V3 is constant product between ticks, LB is constant sum within bins.