# Explain the Difference between a Constant Product and a Stable-Swap AMM ⎊ Path

**Published:** 2025-12-05
**Author:** Greeks.live
**Categories:** Path

---

## Explain the Difference between a Constant Product and a Stable-Swap AMM.

A constant product AMM (x y=k) is designed for volatile asset pairs (e.g. ETH/USDC), resulting in high slippage for large trades.

A stable-swap AMM (e.g. Curve) uses a hybrid function that is nearly flat around the peg, designed for low-volatility, pegged assets (e.g. stablecoins).

This design allows for much larger trades with minimal slippage.

- [How Does a Constant Sum Market Maker (X+y=k) Differ from a Constant Product AMM?](https://learn.greeks.live/path/how-does-a-constant-sum-market-maker-xyk-differ-from-a-constant-product-amm/)

- [What Is the Difference between a Constant Product and a Stable Swap AMM?](https://learn.greeks.live/path/what-is-the-difference-between-a-constant-product-and-a-stable-swap-amm/)

- [How Do “Pegged Assets” Pools, like Stablecoin-to-Stablecoin, Minimize Impermanent Loss?](https://learn.greeks.live/path/how-do-pegged-assets-pools-like-stablecoin-to-stablecoin-minimize-impermanent-loss/)

- [Why Are Stableswap Pools Generally Unsuitable for Volatile, Non-Pegged Asset Pairs?](https://learn.greeks.live/path/why-are-stableswap-pools-generally-unsuitable-for-volatile-non-pegged-asset-pairs/)

- [Explain the Difference between an Inverse Perpetual Swap and a Linear Perpetual Swap in the Context of a De-Peg](https://learn.greeks.live/path/explain-the-difference-between-an-inverse-perpetual-swap-and-a-linear-perpetual-swap-in-the-context-of-a-de-peg/)

- [What Is the Difference between a Constant Product Market Maker and a Constant Sum Market Maker?](https://learn.greeks.live/path/what-is-the-difference-between-a-constant-product-market-maker-and-a-constant-sum-market-maker/)

- [How Does a ‘Hybrid AMM’ (Like Curve’s Stableswap) Combine Features of Constant Product and Constant Sum?](https://learn.greeks.live/path/how-does-a-hybrid-amm-like-curves-stableswap-combine-features-of-constant-product-and-constant-sum/)

- [What Are the Trade-Offs between Earning High Trading Fees in a Volatile Pool versus Minimizing Impermanent Loss in a Stable Pool?](https://learn.greeks.live/path/what-are-the-trade-offs-between-earning-high-trading-fees-in-a-volatile-pool-versus-minimizing-impermanent-loss-in-a-stable-pool/)

## Glossar

### [Stable Hashrate](https://learn.greeks.live/area/stable-hashrate/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Predictability ⎊ A stable hashrate ensures consistent block production times on the base layer, which is a critical input for calculating the expected finality of Layer 2 derivative transactions.

### [Constant Product Component](https://learn.greeks.live/area/constant-product-component/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Component ⎊ The fundamental mathematical element, typically the product of the quantities of two paired assets, $x cdot y = k$, that defines the price curve within a specific Automated Market Maker (AMM) structure common in decentralized cryptocurrency exchanges.

### [Stable Probability Low Gamma](https://learn.greeks.live/area/stable-probability-low-gamma/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Characteristic ⎊ Stable Probability Low Gamma describes an options position profile where the likelihood of the option expiring In-the-Money remains relatively constant, and the rate of change of the option's Delta is minimal.

### [Stable Mining Environment](https://learn.greeks.live/area/stable-mining-environment/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Characteristic ⎊ A Stable Mining Environment is characterized by high operational uptime, minimal stale share rates, and a consistent, low-variance block discovery performance.

### [Stable Price Strategy](https://learn.greeks.live/area/stable-price-strategy/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Objective ⎊ A Stable Price Strategy in derivatives trading is designed to generate returns predicated on the expectation that the underlying cryptocurrency's price will experience minimal movement over a specified period.

### [Constant Product Invariant K](https://learn.greeks.live/area/constant-product-invariant-k/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Constant ⎊ This fundamental mathematical constraint dictates that the product of the reserves in a two-asset pool must remain unchanged before and after any trade execution, excluding fees.

### [Constant Product Invariant](https://learn.greeks.live/area/constant-product-invariant/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Mechanism ⎊ The Constant Product Invariant, fundamentally a mathematical relationship, dictates that for two variables, their product remains constant despite fluctuations in individual values; within automated market makers (AMMs), this principle ensures liquidity is continuously available by adjusting asset ratios.

### [Stable Value Cryptocurrency](https://learn.greeks.live/area/stable-value-cryptocurrency/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Collateralization ⎊ Stable Value Cryptocurrency designs typically rely on over-collateralization, employing mechanisms to maintain a peg to a fiat currency or other stable asset through smart contract enforced reserves.

### [Stable Interest Rate Environment](https://learn.greeks.live/area/stable-interest-rate-environment/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Environment ⎊ A stable interest rate environment is characterized by minimal fluctuations in the cost of borrowing and lending capital within a financial system.

### [Constant Product Vs Sum](https://learn.greeks.live/area/constant-product-vs-sum/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Formula ⎊ The constant product formula, $x cdot y = k$, dictates the pricing mechanism for assets within specific Automated Market Makers (AMMs), ensuring the product of the reserves remains invariant during trades.

## Discover More

### [Explain the Difference between "Real-Time VWAP" and "End-of-Day VWAP"](https://learn.greeks.live/path/explain-the-difference-between-real-time-vwap-and-end-of-day-vwap/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Explain the Difference between "Real-Time VWAP" and "End-of-Day VWAP"](https://learn.greeks.live/wp-content/uploads/2025/10/Asymmetric-Illumination-of-Digital-Asset-Volatility-Surface-Overlays-Financial-Horizon.webp)

Real-time VWAP is a continuously updated intraday metric; end-of-day VWAP is the final, static daily benchmark.

### [What Is the Constant Product Formula (X Y = K) in AMMs?](https://learn.greeks.live/path/what-is-the-constant-product-formula-x-y-k-in-amms/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Constant Product Formula (X Y = K) in AMMs?](https://learn.greeks.live/wp-content/uploads/2025/10/Interlocking-Cross-Structures-Visualizing-Cryptocurrency-Volatility-Surface-Delta-Hedging-Mechanics.webp)

The formula x y = k ensures the product of the two asset reserves remains constant, determining the price.

### [Explain the Relationship between Impermanent Loss and the AMM's Constant Product Formula](https://learn.greeks.live/path/explain-the-relationship-between-impermanent-loss-and-the-amms-constant-product-formula/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Explain the Relationship between Impermanent Loss and the AMM's Constant Product Formula](https://learn.greeks.live/wp-content/uploads/2025/10/Refraction-Dynamics-of-Glass-Geometries-Simulating-Volatility-Surface-Skew-in-Digital-Asset-Options.webp)

The x y=k formula forces the pool to rebalance against external price changes, leading to IL.

### [How Does a Constant Sum Market Maker (E.g. for Stablecoins) Compare to a Constant Product AMM?](https://learn.greeks.live/path/how-does-a-constant-sum-market-maker-e-g-for-stablecoins-compare-to-a-constant-product-amm/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does a Constant Sum Market Maker (E.g. for Stablecoins) Compare to a Constant Product AMM?](https://learn.greeks.live/wp-content/uploads/2025/10/Decentralized-Finance-Protocol-Interface-Depicting-Advanced-Algorithmic-Execution-Mechanism-For-Exotic-Options.webp)

Constant sum (x+y=k) is for pegged assets, offering low slippage near parity, unlike constant product (x · y = k) for volatile assets.

### [Explain the Difference between Cross-Margin and Isolated-Margin and Its Impact on Liquidation Cascades](https://learn.greeks.live/path/explain-the-difference-between-cross-margin-and-isolated-margin-and-its-impact-on-liquidation-cascades/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Explain the Difference between Cross-Margin and Isolated-Margin and Its Impact on Liquidation Cascades](https://learn.greeks.live/wp-content/uploads/2025/10/Metallic-Device-Interface-Probing-Binary-State-Differential-Via-Actuation-Mechanism-in-High-Frequency-Trading.webp)

Isolated-margin limits collateral to one position, containing losses. Cross-margin uses the entire account, allowing one loss to wipe out the whole account and accelerate the cascade.

### [What Happens to the 'K' Value in the Constant Product Formula When a Trade Occurs?](https://learn.greeks.live/path/what-happens-to-the-k-value-in-the-constant-product-formula-when-a-trade-occurs/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Happens to the 'K' Value in the Constant Product Formula When a Trade Occurs?](https://learn.greeks.live/wp-content/uploads/2025/10/Aerodynamic-Composite-Winglet-Structure-Modeling-Volatility-Surface-Implied-Skewness-in-Decentralized-Finance.webp)

The 'k' value increases by the amount of the trading fee, which accrues to the liquidity providers.

### [What Is the Difference between a Futures Contract and a Perpetual Swap?](https://learn.greeks.live/path/what-is-the-difference-between-a-futures-contract-and-a-perpetual-swap-2/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Difference between a Futures Contract and a Perpetual Swap?](https://learn.greeks.live/wp-content/uploads/2025/10/Interlocking-Tangential-Data-Spools-Representing-Decentralized-Finance-Derivative-Contract-Settlement-Mechanisms.webp)

Futures have a fixed expiration date and settlement. Perpetual swaps have no expiration, using a "funding rate" to track the spot price.

### [Explain the Difference between an Inverse Perpetual Swap and a Linear Perpetual Swap in the Context of a De-Peg](https://learn.greeks.live/path/explain-the-difference-between-an-inverse-perpetual-swap-and-a-linear-perpetual-swap-in-the-context-of-a-de-peg/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Explain the Difference between an Inverse Perpetual Swap and a Linear Perpetual Swap in the Context of a De-Peg](https://learn.greeks.live/wp-content/uploads/2025/10/Cryptocurrency-Volatility-Skew-Hedging-Mechanism-Depicting-Exotic-Option-Payoff-Structures.webp)

Linear swap uses the de-pegged stablecoin as collateral (high risk); Inverse swap uses the base asset (e.g. BTC) as collateral (lower risk).

### [What Is the Primary Difference between a Constant Product Market Maker and a Limit Order Book?](https://learn.greeks.live/path/what-is-the-primary-difference-between-a-constant-product-market-maker-and-a-limit-order-book/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Primary Difference between a Constant Product Market Maker and a Limit Order Book?](https://learn.greeks.live/wp-content/uploads/2025/10/Cryptocurrency-Decentralized-Autonomous-Organization-Governance-Orb-Navigating-Volatility-Index-Debris-Fields.webp)

CPMMs use an algorithm for guaranteed liquidity and price discovery, while LOBs rely on explicit buyer/seller orders.

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**Original URL:** https://learn.greeks.live/learn/explain-the-difference-between-a-constant-product-and-a-stable-swap-amm/
