Stable Swap

Unlike constant-product AMMs (x * y = k), stable swaps use a hybrid invariant that combines constant-product and constant-sum formulas. This creates a "flat" region in the middle of the bonding curve where price impact is minimal, allowing large trades near the peg with minimal slippage. The most famous implementation is the StableSwap invariant popularized by Curve Finance.

This is a tunable parameter that controls the shape of the bonding curve. A higher amplification coefficient (A) makes the curve flatter in the middle, approximating a constant-sum curve for low-slippage trades. A lower A makes the curve more like a constant-product AMM, providing more liquidity for assets that drift from their peg. Pools can be optimized by adjusting A based on the correlated assets.

The primary benefit is dramatically reduced slippage for trades between pegged assets. This also results in lower impermanent loss (IL) for liquidity providers compared to traditional AMMs, as the assets in the pool are designed to maintain a stable exchange ratio. However, IL is not eliminated and can become significant if one asset depegs substantially.

Modern stable swap protocols like Curve v2 extend the model beyond pegged assets. They use internal oracles to dynamically adjust the amplification parameter and concentrate liquidity around a moving price range. This allows for efficient trading of correlated assets (e.g., ETH/wBTC) while still benefiting from the low-slippage core mechanism.

Protocols like Curve use a veToken model (vote-escrowed tokens) for governance. Users lock the native token (CRV) to receive veCRV, which grants voting power on pool fee structures and emission gauges that direct liquidity mining rewards. Fees are typically low (often 0.04% or less) and are distributed to liquidity providers and veToken holders.

A canonical example is the Curve 3pool, which contains DAI, USDC, and USDT. Its invariant allows a user to swap 1 million USDT for USDC with minimal price deviation. Key metrics (as of historical peaks) include:

• Total Value Locked (TVL): Often exceeding $10B+
• Daily Trading Volume: Frequently in the hundreds of millions This demonstrates the model's capital efficiency for stablecoin liquidity.

The core innovation is the StableSwap invariant: A * sum(x_i) + D = A * n^n * D + D^(n+1) / (n^n * prod(x_i)). This equation blends a constant sum (for stability) and constant product (for liquidity) curve. The amplification coefficient (A) controls the curve's shape; a higher A creates a flatter curve near equilibrium, reducing slippage for stable assets.

Providing liquidity in a stable swap pool carries significantly lower risk of impermanent loss (divergence loss) compared to a standard CPMM like Uniswap V2. This is because the paired assets are designed to maintain a near-constant exchange ratio. The primary risk shifts to smart contract risk and the depeg risk of the underlying stable assets.

Users deposit paired assets (e.g., USDC/DAI) into a liquidity pool to earn trading fees and often additional liquidity provider (LP) tokens. These LP tokens can be staked in yield farming programs to earn protocol governance tokens as rewards, creating a primary incentive mechanism for deep liquidity.

Stable swaps are integral to cross-chain bridges. When a user bridges a stablecoin from one chain to another, the bridge often uses a stable swap pool on the destination chain to provide the final asset, ensuring the user receives a pegged asset of equal value with minimal price impact.

Protocols like Frax Finance use stable swap pools (e.g., FRAX/USDC) as part of their algorithmic stabilization mechanism. Arbitrageurs trade against the pool to correct deviations from the peg, with the pool's concentrated liquidity providing a strong defense against de-pegging events.

Stable swaps enable low-slippage trading of stablecoins pegged to different fiat currencies (e.g., EURS/USDC, KRW/kUSD), creating a decentralized forex market. They also facilitate the minting and trading of synthetic assets that track real-world prices, using stablecoin collateral pools.

Money market protocols like Curve Lending (LLAMMA) use a stable swap curve as their core liquidation engine. Instead of discrete auctions, undercollateralized positions are gradually converted between collateral and debt via the curve, reducing liquidation penalties and improving user experience.

Decentralized Autonomous Organizations (DAOs) often use treasury assets to provide protocol-owned liquidity (POL) in stable swap pools. This generates consistent fee revenue for the treasury, reduces reliance on external liquidity incentives, and creates a more sustainable liquidity backbone for the ecosystem.

The core risk is vulnerability in the stable swap contract's mathematical implementation or its underlying liquidity pool. A bug could lead to permanent loss of funds. This is amplified by the complexity of the bonding curve and the use of oracles for price feeds in some implementations. Regular audits and formal verification are critical mitigations.

Impermanent loss occurs when the prices of the pooled assets diverge from their intended peg. If one stablecoin depegs significantly (e.g., USDC to $0.90), LPs effectively subsidize arbitrageurs by selling the depegged asset at a loss. The risk is highest for pools containing algorithmic or less-collateralized stablecoins.

Some stable swap implementations (e.g., for cross-asset pools like stETH/ETH) rely on external price oracles to maintain the pool's internal balance. If an oracle is manipulated to report an incorrect price, attackers can drain the pool through arbitrage. This creates a single point of failure external to the core AMM logic.

Many stable swap pools have administrative privileges controlled by a multi-sig or DAO. These keys can adjust critical parameters like fees, amplification coefficient (A), or even withdraw funds in emergencies. This introduces governance risk and the potential for a malicious or compromised admin to exploit the pool.

Stable swaps are foundational DeFi primitives integrated into lending protocols, yield aggregators, and leveraged farming strategies. A failure or exploit in the stable swap can cascade through the ecosystem, causing liquidations and protocol insolvencies elsewhere. This systemic risk is a major consideration for integrators.

Modern stable swaps (e.g., Uniswap V3) use concentrated liquidity, where LPs define a price range. If the price exits this range, the LP's position becomes inactive and earns no fees, while still being exposed to impermanent loss. This requires active management and introduces new vectors for user error and MEV.