Concentrated Liquidity

Concentrated liquidity in Napier allows LPs to allocate funds into bespoke implied-APY ranges, maximizing capital efficiency while minimizing impermanent loss (IL).

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Mechanism

• Similar to Pendle, Napier’s AMM accounts for the natural appreciation of PT toward its underlying as maturity approaches.

  • This mitigates time-dependent IL and ensures that at maturity, LP positions are economically equivalent to holding the underlying asset.

• IL from swaps is further reduced because PT and the underlying are highly correlated.

  • For example, PT-stETH vs stETH trades within a predictable yield range, unlike the higher volatility of spot prices.

• By concentrating liquidity into specific yield bands, LPs can provide much deeper liquidity within realistic ranges (e.g., 0.5–7% APY for staked ETH), enabling larger trades with lower slippage.

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Benefits

• For LPs: Concentration reduces wasted capital, generates dual yield from PT and YT swaps within the same pool, and minimizes IL exposure.

• For Traders: Consolidated liquidity in a single PT/underlying pool ensures greater depth and lower slippage, enabling larger trades with more predictable pricing.

Greater Capital Efficiency

Concentrated Liquidity: Liquidity is allocated within a curator-defined implied APY range, improving capital utilization and increasing LP returns.

Minimal Impermanent Loss (IL)

Napier AMM design ensures that IL is a negligible concern. Napier AMM accounts for PT’s natural price appreciation by shifting the AMM curve to push PT price towards its underlying value as time passes, mitigating time-dependent IL (No IL at maturity).

On top of that, IL from swaps is also mitigated as both assets LP’ed are very highly correlated against one another (e.g. PT-cUSDO / cUSDO). If liquidity is provided until maturity, an LP’s position will be equivalent to fully holding the underlying asset since PT essentially appreciates towards the underlying asset.

In most cases prior to maturity, PT trades within a yield range and does not fluctuate as much as an asset’s spot price. For example, it’s rational to assume that Aave’s USDC lending rate fluctuates between 0%-15% for a reasonable timeframe (and PT accordingly trades within that yield range). This premise ensures a low IL at any given time as PT price will not deviate too far from the time of liquidity provision.

LVR Minimization via Time-Adaptive Curve

In a static curve AMM, the fair PT price rises deterministically as time passes (the discount shrinks), so arbitrage trades are needed to keep up—creating continuous rebalancing costs (LVR).

Napier’s time-adaptive curve internalizes this time decay, reducing the rebalancing costs that would otherwise occur on the path to maturity.

As a result, residual LVR primarily comes from non-deterministic shocks—changes in the market discount rate or PT/YT demand shifts—rather than from the mere passage of time.

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Example

If an LP expects the implied yield of a staked ETH market to remain between 0.5–7%, they can concentrate liquidity within that band.

• This provides higher capital efficiency and stable returns while avoiding unnecessary exposure outside the expected range.

• If yields move beyond 7%, liquidity in that direction becomes thin, limiting further trading until the range is adjusted in a new market.