Buyback & Re-collateralize

The proportion of PUSD collateral in the protocol refers to the real collateral rate of PUST. During minting and redemption, the mortgage rate adjusted in real time according to the algorithm refers to the dynamic mortgage rate of PUST. The proportion of USDT collateral and the collateral rate in the PUST protocol may deviate in some cases, making the agreement's real collateral rate and dynamic collateral rate different.

This can lead to excess collateral in the vault or the need to increase collateral in the vault at the current collateral rate. In order to distribute overcollateralized value to PUST holders or add collateral to the protocol treasury, there are also two special functions in the protocol: re-collateralization and repurchase.

1. Re-collateralize

Anyone can call the recollateralize function to check whether the total value of the collateral in the protocol is lower than the value of the current collateral rate. If so, the protocol allows the caller to exchange the newly minted PEACE with the equivalent of the funds required to achieve the target mortgage rate plus a certain reward rate, and the reward rate is set at 1%. Through the above design, arbitrageurs can be incentivized to quickly narrow the gap and help the protocol achieve the consistency of the real mortgage rate with the target mortgage rate.

$P_{received} = (Y*P_y)(1+B_r)/P_z$

$Y$ is the units of collateral needed to reach the floating collateral ratio

$P_y$ is the price of collateral Y in USD

$B_r$ is the bonus rate for PEACE emitted when recollateralizing

$P_z$ is the price of PEACE in USD‌

2. Re-collateralization Example

Case 1: There are 100 million PUST in circulation at a 50% mortgage rate. The total value of the collateral is 50 million US dollars to achieve the balance of the protocol. When the price of PUST drops to $0.99, the protocol will increase the collateralization rate to 50.25%, and now it takes $250,000 worth of collateral to reach the target collateralization rate.

Anyone can call the re-collateralize function to put up to $250,000 worth of collateral into the collateral pool, and get the equivalent PEACE and an additional 0.5% bonus.

The formula to convert $1/USDT to $3.8/PEACE for $250,000 is as follows:

$PEACE_{received} = \dfrac{(250,000*1.00)(1+0.01)}{3.80}$​

$PEACE_{received} = 66,447.368$

‌ In summary, the arbitrageur will receive up to 66,118.4211 PEACE.

‌3. Buyback

The opposite happens when the share of collateral value in the protocol exceeds the amount required to maintain the target collateralization rate. This can happen in a number of ways:

• The protocol lowered the collateral ratio and successfully kept the PUST price stable.

• The protocol accepts collateral with interest, which increases in value with it.

• Minting and redemption fees are generating revenue.

At this point, any PEACE holder can call the buyback function to exchange the excess collateral value in the system to PEACE, and PEACE will be destroyed by the protocol. This effectively redistributes any excess value back to the holders of PEACE. There is no bonus design for this step, but the process effectively simulates the buyback of shares, which will help reduce the circulation and increase the value of PEACE tokens.

$Collateral_{received} = \dfrac{Z*P_z}{P_y}$

$Z$ is units of PEACE deposited to be burned

$P_z$ is the price of PEACE in USD

$P_y$ is the price of collateral in USD

4. Buyback Example

Case 2: There are 150 million PUST in circulation with a 50% collateralization ratio, and the total value of the collateral is $76 million. There is $1 million worth of excess collateral available for repurchase.

Anyone can call the repurchase function and burn PEACE (worth $1 million) to get the excess collateral.

At a price of $4.2/PEACE and $0.99/USDT, you need to burn 238,095.238 PEACE to obtain the corresponding amount of USDT. Calculated as follows:

$PUSD_{received} = \dfrac{238,095.238*4.20}{0.99}$

$PUSD_{received} = 1,010,101.01$

In summary, the participant will receive up to 1,010,101.01 USDT in the case.

Note: In order to simplify the logic and facilitate the demonstration, the calculation of the re-mortgage fee (0.5%) and the buyback fee (0.5%) is not included in the above case.