Within the earlier article, we in contrast the slippage distinction between curve and uniswap V3 by way of information. We are able to discover that beneath comparable situations, the slippage of uniswap V3 is smaller than that of curve, however some folks wish to know why. So immediately we are going to begin from the technical ideas 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 trade worth has no slippage with restricted liquidity, however as for the fixed product market making curve, the trade worth exists slippage with limitless liquidity. To attain decrease slippage of trade for AMM, curve combines the above two curves and proposes a hybrid market making curve:
A(P0x+y)+xy=okay
Whereby P0 is the balanced worth
y=(k-P0Ax)/(X+A)
Derivation of the above system can get the value
As parameter A approaches infinity
Subsequently, the bigger A , the nearer the trade worth to P0, that’s, the smaller the slippage,
In accordance with the market making curve of uniswap V3,
Derivation of the above system we are able to get the value
m is the magnification issue of x
as parameter m approaches infinity
It may be seen from the above that the trade worth of curve is strongly associated to A, whereas the trade worth of uniswap V3 is strongly associated to m, and we all know that the amplification issue A in curve is set 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. Nevertheless the amplification issue A of curve can’t be infinitely with a view to guarantee infinite liquidity. So the slippage of the curve should be bigger than that of uniswap V3.
https://x3finance.medium.com/why-is-curves-slippage-larger-than-uniswap-v3-e9dd735c88ba
