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Buybacks & Recollateralization

During the operation of QIAN V2, there may be a mismatch between the value of the collateral and the collateral ratio: when the total value of the collateral is less than the current collateral ratio of the system, the collateral needs to be increased; when the value of the collateral exceeds the ratio of the collateral ratio, the excess collateral value can be allocated to KUN holders. To quickly redistribute value back to KUN holders or increase system collateral, two functions are built into the protocol: buyback and recollateralization.
Recollateralization
When the actual collateral ratio of the system is lower than the nominal collateral ratio, the system requires users to replenish the collateral. This process is called recollateralization. Anyone can call the recollateralization function which then checks if the total collateral value in USD across the system is below the current collateral ratio. If it is, the system allows the caller to add up to the amount needed to reach the target collateral ratio in exchange for newly minted KBT at a bonus rate. The bonus rate is set to 0.5% to quickly incentivize arbitragers to close the gap and recollateralize the protocol to the target ratio. The incentive amount can be adjusted through community governance in the subsequent operation of the agreement.
KBTreceived=(Yi∗Pi)(1+Br)PKKBT_{received} = \frac{(Y_i*P_i)(1+B_r)}{P_K}KBTreceived​=PK​(Yi​∗Pi​)(1+Br​)​
Where:
​YiY_iYi​
 is the amount of collateral iii
 required to reach the collateral rate;
​PiP_iPi​
 is the price for collateral iii
 provided by the Chainlink Oracle;
​BrB_rBr​
 is the percentage of the reward KUN minted during recollateralization;
​PKP_KPK​
 is the market price of the KUN token, provided by the weighted average prices of DEX pool.
Example D
Assuming that the system is in a state of insufficient collateral at this time, it needs $500,000 of collateral to reach the target mortgage rate. The user can call the recollateralization function and provide $500,000 worth of collateral to the protocol. At this time, the user can receive KBT tokens equivalent to 500,000×1.05, and the reward amount is 5%.
Placing 500,000 BUSD($1.00/BUSD), the KUN price is $6.00/KUN, the calculation process is as follows:
KBTreceived=(500,000×1.00)(1+0.05)6.00=87,500KBT_{received} = \frac{(500,000×1.00)(1+0.05)}{6.00} = 87,500KBTreceived​=6.00(500,000×1.00)(1+0.05)​=87,500
Buybacks
The opposite scenario occurs when there is excess collateral in the system than required to hold the target collateral ratio. This can happen in several  ways: 
The protocol has been lowering the collateral ratio successfully keeping the price of QSD stable;
Interest bearing collateral is accepted into the protocol and its value accrues;
Minting and redemption fees are creating revenue;
In such a scenario, any KUN holder can call the buyback function to exchange the amount of excess collateral value in the system for KUN which is then burned by the protocol. 
To effectively redistributes excess value back to the KUN distribution and holders, we expect the users to actively participate in buybacks to gain value since there is 1% bonus rate for the buyback function, with the consumption in buyback, KUN also has expectations of value growth. After the buybacks occurs, since some KUN will be burned, it can also bring added value to all KUN holders.
Collaterali, received=K×PKPiCollateral_{i,\ received} = \frac{K×P_K}{P_i}Collaterali, received​=Pi​K×PK​​
Where:
​KKK
 is units of KUN to be burned in buyback;
​PKP_KPK​
 is the market price of the KUN token, provided by the weighted average prices of DEX pool;
​PiP_iPi​
 is the price in USD of collateral iii
, provided by Chainlink Oracle.
QIAN V2 supports a variety of collateral, so when buyback happens, the system will allow users to choose the collateral by themselves. Suppose the amount of certain collateral is completely repurchased and the collateral ratio still cannot return to the target value. In that case, the user can continue to choose other collateral to repurchase until the target collateral ratio is achieved.
Example E
There is 60,000,000 QSD in circulation at a 60% collateral ratio. The total value of collateral across the BUSD, BNB, BTCB pools is 40,000,000 USD. There is 40,000,000 USD worth of excess collateral available for KUN buybacks. In the three kinds of collateral, the total value of the lowest is BTCB(3,700,000 USD). Assuming that a user chooses to exchange BTCB with KUN, then after exchanging all BTCB, the user can still exchange BUSD or BNB with KUN equal to 300,000 USD.
If the user chooses to exchange a BNB equivalent to 4,000,000 USD at the beginning, and the price of BNB is $42.5/BNB and KUN is $10/KUN, then: 
KUNburned=4,000,00010=400,000 KUNKUN_{burned} = \frac{4,000,000}{10} = 400,000\ KUNKUNburned​=104,000,000​=400,000 KUN
BNBreceived=400,000×1042.5=94,117.64705882 BNBBNB_{received} = \frac{400,000×10}{42.5} = 94,117.64705882\ BNBBNBreceived​=42.5400,000×10​=94,117.64705882 BNB