Stablecoin AMM Design in 2026: Curves Built to Hold a Peg

In most explainers the automated market maker is one machine: deposit two assets, a constant-product formula sets the price, and traders swap against the reserves. That picture is accurate for a pool holding Ethereum against a dollar, where the two sides are genuinely expected to drift apart. It is close to wrong for a pool holding one dollar-token against another, where the entire point is that the two sides should never drift apart at all. Designing an AMM for pegged assets means building a market maker that assumes equality right up to the moment equality breaks, and then fails slowly instead of all at once.

That design problem stopped being niche a long time ago. The total supply of stablecoins passed more than $300 billion in 2026, and the deepest on-chain trading pairs are dollar-for-dollar, not speculative. The United States now has a federal statute, the GENIUS Act, that President Trump signed on 18 July 2025 and that dictates what may back a payment stablecoin. None of that law touches the curve. The AMM is still an engineering decision, and the engineering is where pegs are quietly defended or quietly lost.

This piece follows stablecoin AMM design from the math upward: why the constant-product curve is the wrong tool for a dollar, how Curve bends the curve to fix it, what the amplification coefficient actually trades away, how the design behaves when a peg really breaks, and where concentrated liquidity, crvUSD, Fluid and the rest of the 2026 venue map leave the category now.

The constant-product curve treats a dollar like a gamble

Start with the formula that launched the field. In a constant-product pool the reserves of the two tokens, x and y, are held so that x times y equals a constant k. Every trade moves along that hyperbola, so the price shifts with each swap and the price impact grows with trade size. For a volatile pair that behavior is a feature, because the curve is discovering a price nobody knows in advance. For a pair of dollars it is a defect, because the price is already known. It is one.

Work a quick example. Put 1,000,000 USDC and 1,000,000 USDT into a constant-product pool, so k is 1,000,000,000,000. A trader who wants 100,000 USDT pushes the USDT reserve down to 900,000, which forces the USDC reserve up to k divided by 900,000, or about 1,111,111. The trader hands over roughly 111,111 USDC for 100,000 USDT, an effective price near 1.11. That is an 11 percent toll on a trade between two assets that are both meant to be worth exactly one dollar. The slippage is not discovering anything; it is pure friction, and it is a standing invitation for arbitrageurs to pick the pool off whenever the two coins trade even slightly apart.

The deeper flaw is that the constant-product curve spreads liquidity across every price from zero to infinity. For a dollar pair almost all of that range is irrelevant, so almost all of the deposited capital sits idle, and the thin slice of liquidity near one dollar is too shallow to absorb real size without moving. A stablecoin AMM has to concentrate its firepower where it matters, around the peg, and to do that it needs a different curve.

StableSwap: a curve that changes its mind

The canonical answer arrived in 2019, when Curve founder Michael Egorov published the StableSwap whitepaper. His idea was to blend two invariants that each fail on their own. A constant-sum curve, where x plus y is held constant, quotes a perfectly flat price of exactly one and charges zero slippage, which is ideal until you notice that a flat line lets a single trader take all of the good asset out at par; the pool can be emptied of one coin the instant the market price leaves the peg. A constant-product curve never empties and always quotes a price, but wastes capital near the peg. StableSwap interpolates between the two.

Near the balance point the curve behaves almost like constant sum: flat, tight and cheap, so a dollar-for-dollar swap barely moves the price. As the pool tilts toward one asset, the curve bends toward constant product: curved, protective and impossible to fully drain. Egorov described the result as Uniswap with leverage, because a modest amount of capital delivers the depth of a far larger constant-product pool. The invariant that does this is, in plain terms, A times n-to-the-power-n times the sum of the balances, plus the invariant D, set equal to A times D times n-to-the-power-n plus D-to-the-power-(n plus 1) divided by n-to-the-power-n times the product of the balances, where n is the number of coins, the balances are the pool reserves, D is the total balanced value, and A is the amplification coefficient that controls everything.

By 2026 this design is the backbone of on-chain dollar trading. Curve reported that the number of its latest StableSwap-NG pools on Ethereum crossed 1,000 in July 2026, and the protocol still anchors the deepest USDC, USDT and DAI pairs on Ethereum and most layer twos. The curve that started as a research PDF now moves a meaningful share of every dollar that changes hands on-chain.

The amplification coefficient is a risk dial, not a performance dial

Everything interesting about a StableSwap pool lives in A, the amplification coefficient. A high A, in the hundreds or low thousands, makes the curve extremely flat near the peg: tiny slippage, enormous effective depth, the kind of execution that lets a trader move eight figures between two dollars for a few basis points. A low A keeps more curvature near the peg, charging more slippage but reacting sooner when one asset starts to slip. Curve operators can even ramp A up or down over time through governance, tightening the curve when confidence is high and loosening it when a pair looks shaky.

The point that gets lost in the marketing is that A is a risk dial, not a free performance dial. The flat region that delivers beautiful execution is the same region in which the pool will hand out its good dollars cheaply if the peg ever genuinely breaks. A high-A pool is a strong statement that the peg will hold; a low-A pool hedges that bet. In a stablecoin AMM, the capital efficiency everyone celebrates is identical to peg-break exposure. You cannot buy one without buying the other. This is the stablecoin analogue of impermanent loss, and it is the reason a stable pool is never the risk-free yield it looks like on a dashboard.

StableSwap is the most common design, but it is not the only one. The table below lays out the main invariant families a stablecoin pool can use, what each does when the pair is trading at par, and how each behaves when one side slips.

When the peg breaks: the one-sided drain

To understand why stablecoin AMMs matter, watch one fail. The failure mode is always the same shape. When the market price of one token in the pool moves away from a dollar and stays there, arbitrageurs do exactly what the curve invites: they sell the cheap, de-pegged token into the pool and pull out the token still worth a dollar, repeating until the pool holds almost nothing but the bad coin. The liquidity providers are left holding the asset nobody wants. On a high-A curve this happens quickly, because the curve stays flat and cheap right up until the pool is badly imbalanced. It is not a malfunction; it is the curve quoting a continuous price the whole way down. The consequence is that a stablecoin LP is structurally short the peg, collecting small fees in calm weeks and absorbing the loss when a peg fails.

Terra’s UST showed the pure version in May 2022. UST was algorithmic, backed not by reserves but by a mint-and-burn arbitrage with its sister token LUNA, and its liquidity backbone on Ethereum was Curve. On 7 May, Terraform Labs withdrew 150 million UST from Curve’s 3pool as part of a planned migration to a new pool. Thirteen minutes later a trader swapped 85 million UST for USDC, and more size followed. The withdrawal had thinned the curve at the worst possible moment; the pool tilted, UST slipped under a dollar, and the StableSwap curve did precisely what it is built to do, letting arbitrageurs pull the good dollars out and leave UST behind.

From there the reflexive mechanics took over. UST fell to about $0.75 within two days, collapsed into the $0.20s by the middle of the following week, and traded below $0.10 by 13 May, with roughly $40 billion of combined UST and LUNA value erased inside a week. The lesson for AMM design is blunt: a stablecoin AMM transmits a depeg, it cannot prevent one. The curve is only ever as good as the thing it is pricing, and no amount of clever math backstops a peg with nothing behind it.

USDC and the Silicon Valley Bank weekend

A reserve-backed coin can break too, for reasons the curve cannot see. On 11 March 2023 Circle disclosed that $3.3 billion of USDC reserves were trapped at the failed Silicon Valley Bank. USDC, a fully fiat-reserved stablecoin, fell to about $0.87 on Coinbase and on Curve as holders scrambled to swap into USDT and anything else. The on-chain pools became the real-time price of fear. Curve’s 3pool tilted heavily toward USDC as traders dumped it, and the curve quoted the widening discount continuously, second by second, while centralized venues throttled withdrawals. The peg snapped back only after US regulators guaranteed all SVB depositors on 12 March.

Two design lessons come out of that weekend. First, even a safe, fully-backed stablecoin can depeg on off-chain news the AMM has no way to observe, which means no curve shape can be trusted to hold a peg by itself. Second, the pool behaved exactly as designed, absorbing one-sided flow and pricing the risk in the open. That is both its value and its danger: it provided continuous, honest liquidity precisely when exchanges were gating redemptions, and it left its liquidity providers long a discounted coin when the music stopped. The dependence of the dominant stablecoins on off-chain bank reserves is the one risk the curve cannot engineer away, which is exactly the gap US law would later move to close.

A depeg playbook for pool designers

Different stablecoins break for different reasons, and a good pool designer treats each failure as a distinct engineering case rather than one generic risk. The table maps the main triggers, a real example of each, how a naive high-A pool responds, and the design levers that soften the blow.

The bridge row deserves a flag of its own. A wrapped or bridged dollar can depeg from its native version even when the issuer is perfectly healthy, simply because the bridge holding the collateral is compromised or congested, which turns cross-chain dollar liquidity into a security question as much as a pricing one. It is one more reason the richest honeypots in crypto have been the bridges that move stablecoins between chains.

Concentrated liquidity meets the peg

Uniswap took a different route to the same goal. Rather than inventing a special curve, Uniswap V3 introduced concentrated liquidity in 2021, letting liquidity providers place ordinary constant-product liquidity inside a price range of their choosing. For a dollar pair, an LP simply concentrates everything into a razor-thin band around one dollar, which reproduces most of StableSwap’s depth using a general-purpose engine. Uniswap also added a one-basis-point fee tier aimed squarely at stable pairs, and Curve answered by cutting its own fee to one basis point in 2022.

By 2026, Uniswap V4, which launched on 31 January 2025 with hooks and a single-contract architecture, runs tick-aligned stable pools that match or beat Curve on mainstream dollar pairs up to around a quarter of a million dollars per trade. For very large stable swaps, Curve’s purpose-built curve still gives up less slippage. The trade-off is the familiar one in a new costume: concentrated liquidity at the peg is dazzlingly capital-efficient, but a position goes out of range and stops both earning fees and providing depth the instant the peg actually moves, which is the exact moment depth is most needed. The risk did not disappear; it changed shape.

Not every dollar is the same dollar

A curve cannot be designed well without knowing what kind of dollar it is pricing, because each type of stablecoin breaks for a different reason and at a different speed.

• Fiat-reserved: USDT, the largest at roughly $184 billion, and USDC at around $75 billion, backed by cash and short Treasuries. Their depeg risk is off-chain: a bank failure or a frozen reserve.
• Overcollateralized and crypto-backed: Sky’s USDS and the original DAI, together around $13 billion, plus Curve’s own crvUSD. Backed by crypto worth more than the debt; the risk is a collateral crash and the liquidation that follows.
• Synthetic and delta-neutral: Ethena’s USDe, whose supply sat near $4.7 billion in 2026 after contracting sharply from a 2025 peak, backed by hedged derivatives positions whose risk is funding and exchange solvency.
• Yield-bearing and RWA-backed: tokenized Treasury funds and savings tokens that are meant to accrue value, so an AMM pricing them against a flat dollar must center on a deliberately moving target, not on 1.00.
• Algorithmic: UST and its imitators, defended only by reflexive token mechanics, a category the market abandoned after 2022.

The design implication is direct. Two fiat-reserved coins can share a high-A pool with reasonable confidence. A yield-bearing token paired against a plain dollar needs a curve built around a drifting price rather than a fixed peg, or it will leak the accrued yield to arbitrageurs every day. Anything paired against a synthetic dollar is pricing a tail risk the curve cannot hedge, and belongs in its own isolated pool with conservative parameters. The invariant is universal; the parameters are a judgment about the specific coin.

crvUSD and LLAMMA: the AMM as a liquidation engine

The most inventive thing Curve has done with the AMM is point it at a job other than trading. Its own stablecoin, crvUSD, launched in 2023 and manages loan risk through a mechanism called the Lending-Liquidating AMM Algorithm, or LLAMMA. Instead of a single liquidation price, a borrower’s collateral is spread across a set of price bands, ten by default and adjustable from four to fifty. As the collateral price falls into that range, the AMM continuously converts collateral into crvUSD, band by band, a process Curve calls soft liquidation; if the price recovers, it converts the crvUSD back into collateral, a de-liquidation. A position is hard-liquidated only if its health keeps deteriorating.

In practice, positions have been observed sitting in soft liquidation for a median of roughly two weeks, and occasionally for months at a time. The gentleness is real, and so is its cost: LLAMMA’s constant rebalancing realizes a loss on every swing while a position is inside its band, so a borrower who is repeatedly pushed in and out of the range pays for the smoothness. It is the clearest case in DeFi of an AMM curve doing something other than swapping two tokens. Here the curve is a risk manager, turning the same math that quotes a price into a mechanism that unwinds a loan a sliver at a time, which is also why crvUSD can hold its own peg without a traditional, cliff-edge liquidation cascade threatening it.

Fees, LVR, and who really earns on a stable pool

The pitch for stable pools is low-risk yield. The design says something more honest. Even a dollar pool suffers loss-versus-rebalancing, or LVR: whenever the true price of the pair moves, even by a hair because one coin trades slightly rich on a centralized exchange, arbitrageurs capture the gap and the liquidity providers eat it. The a16z crypto research team of Jason Milionis, Ciamac Moallemi, Tim Roughgarden and Anthony Lee Zhang formalized the idea and landed on a line worth keeping: “An AMM can be successful only if it has happy LPs, which means that fee revenues need to scale with LVR.”

On a stable pair the LVR is tiny in a calm week, which is exactly why fees have been competed down to a single basis point. The problem is that LVR spikes during a depeg, the one moment the fees cannot cover it. Layer the economics of 2026 on top. Uniswap’s fee switch, live since late 2025, now routes a slice of LP fees to the protocol. Emissions-driven venues pay providers in governance tokens whose value can evaporate. And the base return on a dollar is, by construction, close to the risk-free Treasury rate the reserves are parked in. Stripped of the marketing, a stable LP is being paid a few basis points to underwrite a rare, large loss. That can be a sound trade; it is not a free one, and it is not the same thing as a savings account.

The curve is only as safe as the code under it

A beautiful invariant still executes as a smart contract, and the contract is where money actually leaves. On 30 July 2023 several Curve stable pools were drained, not because of a flaw in the StableSwap math but because of a reentrancy bug in specific versions of the Vyper compiler that failed to lock the affected functions. Attackers manipulated pool balances and took an estimated $70 million across Curve and protocols that depended on it, before whitehats and negotiations clawed the net loss back to around $52 million.

The episode is the standing reminder that stablecoin AMM security is a stack, not a single curve: the invariant, the implementation that encodes it, the oracle the pool may feed or read, and the bridges that deliver the tokens into it. Each layer is a separate attack surface, and the depeg of a coin inside a pool can be caused by any of them, not just by the issuer. It is also why the largest venues lean so heavily on repeated audits and outsized bug bounties, a field where crypto has paid white-hat researchers sums that dwarf anything in mainstream software. A perfect curve on buggy code is still an empty pool.

The GENIUS Act regulates the reserve, not the curve

The United States finally has a stablecoin statute. The GENIUS Act, which President Trump signed on 18 July 2025, requires issuers of payment stablecoins to hold at least one dollar of permitted reserves (cash, demand deposits, short-term Treasury bills and Treasury-backed repos) for every dollar in circulation, to disclose those reserves every month, and to submit to independent examination. Read against the SVB weekend, the law is a direct patch: it puts a floor under the one thing the curve cannot see, the quality of the reserve behind the token.

What the statute does not do is touch the AMM. The SEC, which had sent Uniswap Labs a Wells notice in 2024, closed that investigation with no enforcement action in February 2025, and no US rule today prescribes how a pool’s curve must be shaped. In the European Union, MiCA regulates stablecoin issuers through its e-money-token and asset-referenced-token categories but likewise leaves the mechanism to engineers. The practical effect on design is subtle but real: as the underlying dollars become safer and more uniform, pools can justify running higher amplification with more confidence. Meanwhile the fight over who gets to keep the yield those reserves throw off is playing out separately, in law and in protocol governance. The curve stays a private engineering choice sitting on an increasingly public asset.

The 2026 stablecoin-AMM landscape

Put the venues side by side and the shape of the market is clear. The figures below are whole-protocol totals across all pairs, not stablecoin-only, but the role each venue plays in dollar trading is what the final column captures. All numbers come from a mid-October 2026 survey of the largest liquidity pools.

Curve’s total value locked looks small next to Uniswap’s volume because stable-pool capital turns over slowly; depth is the product, not churn. The category’s center of gravity is drifting toward hybrids such as Fluid, which lets the same dollars earn lending interest and swap fees at once, and toward concentrated liquidity, yet Curve still owns the deepest dedicated dollar pools. Most users never choose a pool at all. A router or an in-wallet aggregator picks the venue, which is why onboarding and routing quietly decide where stable liquidity actually lives. The token market tells its own story: CRV traded near $0.34 in October 2026, a reminder that owning a category by depth has not translated into owning it by market value.

What a good stablecoin curve is really optimizing for

Every design decision in this field reduces to a triangle: slippage (how cheap a near-peg trade is), capital efficiency (how little liquidity sits idle), and peg-break safety (how gracefully the pool fails when the peg goes). StableSwap’s amplification coefficient, Uniswap’s range width and LLAMMA’s bands are all the same choice wearing different clothes, a single question asked three ways: how much should the pool bet that the peg holds? Push for cheaper trades and tighter capital, and you are quietly shortening the fuse on the day the peg breaks.

The direction of travel in 2026 is to make that bet smarter rather than simply larger: dynamic fees and dynamic amplification that widen with volatility, hooks that can stretch a range or pause a pool when an oracle diverges, and hybrid liquidity that keeps idle dollars working. The macro backdrop is a tailwind. Michael Egorov, who wrote the paper that started all of this, argues the category is crossing a threshold. “By the end of 2026,” he said in February, “I expect that the world at large will come to view stablecoins as an assumed layer of financial infrastructure, with the main topic of interest being how to build on top of them.”

If he is right, the stablecoin AMM stops being a DeFi curiosity and becomes a settlement rail, and the quality of its curve stops being a liquidity provider’s private problem and becomes everyone’s. Hayden Adams, who built the first version of Uniswap, likes to say that AMMs are, in his words, “only just getting started.” On the stablecoin side of the ledger, where a curve now has to double as a liquidation engine, a shock absorber and a payments backbone, the engineering is still catching up to the ambition.

Frequently Asked Questions

Why do stablecoins use a different AMM curve than other tokens?

Because a stablecoin pool assumes both assets are worth the same, the constant-product curve used for volatile pairs wastes capital and forces needless slippage near the peg. Designs like Curve’s StableSwap keep the price nearly flat around the peg and only add curvature as the pool tilts, which gives far deeper liquidity for a dollar-for-dollar trade using the same capital.

What is the amplification coefficient in a stablecoin pool?

The amplification coefficient, written as A, controls how flat a StableSwap curve is near the peg. A high A means very low slippage and high capital efficiency but less protection if the peg breaks, while a low A adds slippage near the peg but reacts sooner when one asset de-pegs. Choosing A is essentially choosing how strongly to bet that the peg will hold.

What happens to liquidity providers when a stablecoin depegs?

The curve lets arbitrageurs buy the still-valuable dollar out of the pool and leave the de-pegged token behind, so providers end up holding the weak asset. That is why a stablecoin liquidity provider is structurally short the peg, earning small fees in calm periods and absorbing a large loss when a peg fails, as happened to UST pools in 2022 and USDC pools during the Silicon Valley Bank weekend in 2023.

Is providing liquidity to a stablecoin pool risk-free?

No. Even near-peg pools face loss-versus-rebalancing and smart-contract risk, fees have been competed down to roughly one basis point, and the base return is close to the Treasury rate backing the reserves. A stablecoin provider is paid a few basis points to underwrite a rare but large depeg loss, which can be a reasonable trade but is not free yield.

Does the GENIUS Act regulate stablecoin AMMs?

No. The GENIUS Act, signed in July 2025, governs stablecoin issuers and their reserves, requiring one-to-one high-quality backing and monthly disclosure. It does not dictate how an AMM curve is built, and the SEC closed its Uniswap investigation in early 2025 without action, so pool design remains an engineering choice.

Yuki Tanaka covers DeFi market structure and on-chain infrastructure for HOGE Wire.