Uniswap v3

01 · Concept — what problem does it solve?

In v2, liquidity is spread along the entire price curve from 0 to ∞ — most of it never touched. v3 lets each LP choose a price range and concentrate capital there, earning fees only while price is inside it. The same depth can be provided with up to ~4000× less capital. The cost: LPing stops being passive. Range selection is an active view on volatility — v3 LPs are functionally short gamma.

02 · Mechanics

• Ticks: price space is discretized as powers of 1.0001; positions are defined between two ticks.
• Virtual reserves: inside a range the pool behaves like a v2 pool with much larger "virtual" reserves — hence the efficiency gain.
• Positions as NFTs: every (range, amount) tuple is unique, so positions are non-fungible — breaking v2-style passive LP composability.
• Fee tiers: 0.01% / 0.05% / 0.30% / 1% pools per pair; LPs select the tier matching the pair's volatility.
• Out of range: position converts fully into one asset and earns nothing until price returns.

03 · Formulas

// tick i ↔ price
P(i) = 1.0001ⁱ

// liquidity L in range [Pa, Pb] at price P
x = L·(√Pb − √P) / (√P·√Pb)
y = L·(√P − √Pa)

// capital efficiency vs v2 (range [Pa,Pb])
eff = 1 / (1 − (Pa/Pb)^¼)   → ~4000× at ±0.05%

04 · Edge cases & risks

• Amplified IL — concentration multiplies divergence loss inside the range; narrow ranges are leveraged short-volatility positions. See Impermanent Loss.
• LVR / informed flow — fast arbitrageurs rebalance the pool against stale prices; passive v3 LPs systematically lose to them (loss-versus-rebalancing).
• JIT liquidity — bots add a razor-thin range one block before a whale swap, capture the fee, withdraw — diluting honest LPs.
• Oracle subtlety — v3 TWAPs use geometric mean of ticks; thin-liquidity tails make manipulation cheaper than v2's full-range depth.