Definition
An AMM curve is a deterministic pricing mechanism that maps the relationship between token reserves in an automated market maker pool and the implied exchange rate between those tokens. It is expressed as a mathematical function or invariant that must remain satisfied before and after each trade. By enforcing this function, the AMM curve governs how prices update as liquidity is added, removed, or traded against.
Different AMM designs implement different curves to target specific market behaviors, such as constant product, constant sum, or hybrid formulations. The shape of the AMM curve directly determines how sensitive prices are to trade size, how liquidity is distributed across price ranges, and how slippage manifests for traders interacting with the pool.
Context and Usage
Within an AMM, the curve serves as the core mechanism that replaces traditional order books by algorithmically quoting prices from on-chain liquidity. The curve’s parameters and functional form encode the pool’s risk profile, capital efficiency, and responsiveness to imbalances between token reserves. Because it is fully specified and transparent, the AMM curve allows on-chain participants to anticipate how prices will move for any hypothetical trade size.
In decentralized finance, AMM curves are used to formalize pricing for spot swaps, stable-asset pairs, and more specialized liquidity configurations. Protocol designers select or customize an AMM curve to align with the intended use case, such as minimizing price deviation for correlated assets or supporting wide price ranges for volatile pairs. As a mechanism, the AMM curve is central to how AMM-based markets discover prices and manage on-chain liquidity.