How Does a Stablecoin Pool’s Formula Differ from the Constant Product Formula?
Stablecoin pools often use a "stableswap" or hybrid formula, which combines the constant product and constant sum formulas. This results in a much flatter curve around the 1:1 peg, allowing for very low slippage on trades near the peg.
However, as the price diverges significantly from the peg, the curve reverts to the constant product model to ensure deep liquidity, though with higher slippage.
Glossar
Constant Product Model
Algorithm ⎊ The Constant Product Model is the seminal algorithm for Automated Market Makers, defining the relationship between two asset reserves, $x$ and $y$, such that their product remains constant, $x cdot y = K$.
Constant Sum Formula
Mechanism ⎊ The Constant Sum Formula, sometimes employed in specialized stablecoin AMMs, dictates that the sum of the reserves ($x + y = k$) remains fixed, implying a constant marginal price of one-to-one regardless of the trade size.
Constant Product
Invariant ⎊ The core principle dictates that the product of the quantities of the two assets in a liquidity pool remains constant, represented mathematically as $x cdot y = k$, where $x$ and $y$ are the reserves of the two tokens.