Swap Slippage

The swap slippage is given by:

Sij=Si+(Sj)=SiSjS_{i \rightarrow j} = S_i + (-S_j) = S_i - S_j


Si=g(ri)g(ri)ririS_i = \dfrac{g(r'_i) - g(r_i)}{r'_i - r_i}
ri+rir'_i + r_i

If the swap amount is small, the slippage can be give by

Sij=g(ri)g(ri)S_{i \rightarrow j} = g'(r_i) - g'(r'_i)

Practical example of slippage calculation

We take the coverage ratio of USDT at 0.909 and ETH at 1.033. Working this out, we’d get:


g(0.909)=0.0000270.9098=0.03%g'(0.909) = -\dfrac{0.00002*7}{0.909^8} = 0.03\%


g(1.033)=0.0000271.0338=0.01%g'(1.033) = -\dfrac{0.00002*7}{1.033^8} = 0.01\%

Hence we have

SUSDTETH=0.03%0.01%=0.02%S_{USDT \rightarrow ETH} = 0.03\% - 0.01\% = 0.02\%

This represents the marginal slippage when someone is performing a small amount of swap at this coverage ratio. And yes, the slippage is positive and user can benefit from the swap!

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