Within the earlier article, we in contrast the slippage distinction between curve and uniswap V3 via knowledge. We are able to discover that underneath comparable situations, the slippage of uniswap V3 is smaller than that of curve, however some folks wish to know why. So at the moment we’ll begin from the technical rules of curve and uniswap to research why the slippage of the curve is bigger than that of uniswap V3. As everyone knows, curve adopts the blended curve equation of fixed product and fixed sum. As for the fixed sum market making curve, the alternate value has no slippage with restricted liquidity, however as for the fixed product market making curve, the alternate value exists slippage with limitless liquidity. To realize decrease slippage of alternate for AMM, curve combines the above two curves and proposes a hybrid market making curve:
A(P0x+y)+xy=ok
Whereby P0 is the balanced value
y=(k-P0Ax)/(X+A)
Derivation of the above components can get the value
As parameter A approaches infinity
Due to this fact, the bigger A , the nearer the alternate value to P0, that’s, the smaller the slippage,
Based on the market making curve of uniswap V3,
Derivation of the above components we will get the value
m is the magnification issue of x
as parameter m approaches infinity
It may be seen from the above that the alternate value of curve is strongly associated to A, whereas the alternate value of uniswap V3 is strongly associated to m, and we all know that the amplification issue A in curve is decided internally by the protocol and can’t be modified by exterior customers, whereas the amplification issue m of uniswap V3 is totally decided by the value vary set by the exterior liquidity supplier. In different phrases, the amplification issue m can theoretically be infinitely. Nonetheless the amplification issue A of curve can’t be infinitely to be able to guarantee infinite liquidity. So the slippage of the curve have to be bigger than that of uniswap V3.
https://x3finance.medium.com/why-is-curves-slippage-larger-than-uniswap-v3-e9dd735c88ba
