How Curve's StableSwap Works: Amplification, Low Slippage and Depeg Risk

The stableswap amplification curve is the pricing formula Curve uses to swap assets that are supposed to trade near a fixed ratio, such as USDC against USDT or stETH against ETH. Instead of the standard x*y=k constant-product curve, StableSwap blends a flat constant-sum line (which gives perfect 1:1 pricing) with the familiar product curve (which guarantees liquidity never runs dry). A single tunable parameter, the amplification coefficient A, decides how much of each behavior you get. The result is a pool that quotes prices extremely close to par across most of its range, then degrades into normal AMM behavior only when reserves become badly lopsided. Below we walk through why that works, what A actually changes, and the specific risk it hands to liquidity providers during a depeg.

Why Curve-style stable pools offer near-zero slippage

In a normal x*y=k pool, every trade moves along a hyperbola, so even small swaps shift the price because the curve is permanently bent. That bend is wasteful when both assets are meant to be worth the same. If a dollar of USDC always equals a dollar of USDT, you want the pool to quote 1:1 no matter how much trades, and a perfectly flat constant-sum line (x+y=k) does exactly that. The problem is that a pure constant-sum line lets one asset be fully drained, leaving the pool empty and the peg unenforced.

StableSwap's insight is to behave like the flat line in the middle, where reserves are roughly balanced and almost all trading happens, while bending back toward the constant-product curve near the edges so the pool can never be emptied. That is why swapping ten million dollars of stablecoins through a deep Curve pool can cost a few basis points instead of a percentage point. If you want the broader product context first, see our explainer on what Curve Finance is and the practical step-by-step swap tutorial.

How the amplification coefficient (A) blends the two curves

The amplification coefficient is the dial that sets where the flat zone ends and the bend begins. Mathematically, A multiplies the constant-sum portion of the invariant relative to the constant-product portion. When A is very large, the constant-sum term dominates and the curve is nearly flat across a wide band of reserve ratios, so prices stay glued to par. When A approaches zero, the constant-sum term vanishes and StableSwap collapses back into a plain x*y=k product curve.

Crucially, A is a finite blend, not an on/off switch. The flat zone is only an approximation: every pool still bends, and a higher A simply pushes the bend further out toward the extremes. The trade-off is that the same A that flattens the center also makes the eventual bend steeper, so once the pool does tip out of balance the price impact arrives faster. This is conceptually related to concentrated liquidity: in both cases you are packing depth into the price range you expect to trade in, and accepting worse behavior outside it.

Walking the curve from balanced to imbalanced

Start with a pool holding equal reserves, say 10 million USDC and 10 million USDT. Here you sit in the dead center of the flat zone, where the marginal price is essentially 1.000. A trader can sell a large amount of USDC and still receive almost exactly the same amount of USDT, because the curve barely tilts. With a high A, this flat region stretches a long way, so the pool absorbs big trades with minimal price impact.

Now keep selling USDC into the pool. As USDC reserves swell toward 16 or 17 million and USDT drains toward 3 or 4 million, you approach the edge of the flat zone. Here the curve bends hard. The price the pool offers for additional USDC drops quickly, and each extra unit you sell costs more in slippage than the last. A higher A delays this moment but makes the bend steeper once it hits. So A does not remove slippage; it relocates it, concentrating depth where assets are near par and concentrating pain at the extremes.

The stableswap amplification curve and what happens when an asset depegs

This geometry is exactly why a depeg is so costly for liquidity providers. Suppose the pool holds USDC and a stablecoin that suddenly loses its peg and starts trading at 90 cents on external markets. Rational traders will dump the cheap, broken stablecoin into the Curve pool and pull out the still-healthy USDC, because the pool's flat zone keeps offering close to 1:1 until reserves get badly skewed. Arbitrage continues until the pool's internal price finally catches up to the real 0.90 market price, which only happens deep in the steep part of the curve.

By then the pool has been emptied of the good asset and stuffed full of the bad one. As an LP you do not get to choose; your share of the pool is now overwhelmingly the depegged token. You effectively sold your healthy USDC for a discount and were left holding the loser. This is a more severe cousin of ordinary impermanent loss, and it is the core reason to understand stablecoin depeg risk before providing liquidity to any stable pool.

StableSwap vs a standard x*y=k AMM in practice

Against a plain constant-product AMM, StableSwap wins decisively for assets that genuinely hold a peg, because it concentrates almost all of its depth at the 1:1 price most trading actually happens at. A constant-product pool spreads liquidity uniformly across all prices from zero to infinity, which is the right design for volatile pairs like ETH against a stablecoin but wasteful for a USDC/USDT pair that should never stray far from par.

The flip side is that StableSwap's advantage is conditional on the peg holding. The constant-product curve, by spreading depth thin, naturally rebalances its holdings across the full price range and never bets that two assets stay equal. StableSwap makes that bet explicitly through A, so it is faster and cheaper in the normal case and more exposed in the abnormal one. The right tool depends entirely on whether you expect the two assets to remain pegged.

What this means for stablecoin and LST traders

If you are swapping, the takeaway is simple: stable pools are the cheapest venue for like-for-like pegged assets, and the deeper and more balanced the pool, the closer you trade to par. Check the pool's current reserve balance before a large swap, because a pool already skewed toward the asset you are selling will be sitting closer to the steep edge and quote you a worse rate. For liquid staking tokens such as stETH or rETH against ETH, the same logic applies, with the added nuance that these assets carry a small built-in rate that the pool and its A parameter are tuned to accommodate.

If you are providing liquidity, treat A as a statement of conviction. A high-A pool pays you tight, frequent fees while the peg holds and hands you the bad asset if it breaks. Size your exposure to your confidence in the weakest asset in the pool, not the strongest, and remember that the same amplification that makes the pool feel safe in calm markets is what concentrates your losses in a depeg.

This article is for educational purposes only and is not financial advice.