HackMDFlashloan fee of Uniswap v2
tags: uniswap flashloan fee uniswap-v2
Refer to Uniswap v2 Whitepaper, each swap should satisfy following formula:
\[ (x_1 - 0.003 \cdot x_{in}) \cdot (y_1 - 0.003 \cdot y_{in}) \ge x_0 \cdot y_0 \tag{1} \]
To simplify the calculation on-chain:
\[ (1000 \cdot x_1 - 3 \cdot x_{in}) \cdot (1000 \cdot y_1 - 3 \cdot y_{in}) \ge 1000000 \cdot x_0 \cdot y_0 \tag{2} \]
When we flash loan from Uniswap v2 pair, what is the amount including fee we should repay?
Suppose we flash loan amount of token \(y\): \(y_{out}\).
\(x_{in}\) and \(y_{in}\) are the amount of token \(x\) and token \(y\) to repay.
\(x_0\) and \(x_1\) are the balance of token \(x\) before and after flash loan, respectively, \(y_0\) and \(y_1\) are the balance of token \(y\) before and after flash loan.
The problem is to calculate \(y_{in}\) using \(y_{out}\).
Since we don't flash loan token \(x\), so \(x_{in} = 0\), \(x_{out} = 0\), \(x_0 = x_1\), we can simplify formula (2):
\[ 1000 \cdot y_1 - 3 \cdot y_{in} \ge 1000 \cdot y_0 \tag{3} \]
\[ y_1 - y_0 \ge \frac{3}{1000} \cdot y_{in} \tag{4} \]
The relation between \(y_{in}\) and \(y_{out}\) is:
\[ y_{in} = y_1 - ( y_0 - y_{out}) \tag{5} \]
Using formula (4) and (5):
\[ y_{in} - y_{out} \ge \frac{3}{1000} \cdot y_{in} \tag{6} \]
We can calculate \(y_{in}\):
\[ y_{in} \ge \frac{1000}{997} \cdot y_{out} \tag{7} \]
In Solidity contract, to avoid rouding down error, we should add 1 to round up:
where repayAmount is \(y_{in}\), amountOut is \(y_{out}\).
So the flashloan fee of Uniswap v2 is:
\[ \frac{1000}{997} - 1 \approx 0.0030090271 \approx 0.30090271\% \tag{8} \]
