Borrowing Logics

Here the logics used in Borrowing contract and BorrowLib are explained.

In code, many base PRECISION are used to avoid, arithmetic, division or modulo by zero errors.

USDa to mint

borrowing.sol

function _transferToken(
        address _borrower,
        uint256 amount,
        uint128 _ethPrice,
        uint256 optionFees
)

Param Name	Param Type	Description
_borrower	address	Address of the borrower.
amount	uint256	Deposited ETH amount.
_ethPrice	uint128	Current ETH price.
optionFees	uint256	Options fees to deduct from borrower.

uint256 tokensToLend = BorrowLib.tokensToLend(amount, _ethPrice, LTV);
bool minted = usda.mint(_borrower, (tokensToLend - optionFees));

BorrowLib.sol

function tokensToLend(
        uint256 depositedAmont, 
        uint128 ethPrice, 
        uint8 LTV
    ) public pure returns(uint256){
        uint256 tokens = (depositedAmont * ethPrice * LTV) / (USDA_PRECISION * RATIO_PRECISION);
        return tokens;
}

Calculate the USDa to lend, by using LTV ratio. Then deduct the options fees, mint the remaining to borrower and options fees to treasury.

Functions which are using the above logic

• Borrowing Deposit.

LTV is global variable in Borrowing contract.

ABOND to mint

borrowing.sol

function _mintAbondToken(
        address _toAddress, 
        uint64 _index, 
        uint256 _amount
)

Param Name	Type	Description
_toAddress	address	Address of the borrower.
_index	uint64	For which position index needs to mint ABOND.
_amount	uint256	ETH backed.

uint128 amount = BorrowLib.abondToMint(_amount,bondRatio);

BorrowLib.sol

function abondToMint(
        uint256 _amount, 
        uint64 _bondRatio
) public pure returns(uint128 amount){
        amount = (uint128(_amount) * USDA_PRECISION)/_bondRatio;
}

Calculate the ABOND to mint to user during withdraw based on bondRatio and mint it to borrower.

Functions which are using the above logic

• Borrowing Withdraw.

Normalized amount calculation

borrowing.sol

uint256 normalizedAmount = BorrowLib.calculateNormAmount(tokensToLend,lastCumulativeRate);

BorrowLib.sol

function calculateNormAmount(
        uint256 amount,
        uint256 cumulativeRate
) public pure returns(uint256){
        return (amount * RATE_PRECISION)/cumulativeRate;
}

Calculate the normalized amount by dividing the total borrowed amount with cumulative rate. Cumulative rate should get from calculateCumulativeRate method.

Functions which are using the above logic

• Borrowing Deposit.

ABOND USDa Pool Calculation

borrowing.sol

uint256 discountedETH = BorrowLib.calculateDiscountedETH(
    depositDetail.depositedAmount,
    _ethPrice
    );

BorrowLib.sol

function calculateDiscountedETH(
        uint256 amount,
        uint128 ethPrice
    ) public pure returns(uint256){
        return ((((80*calculateHalfValue(amount))/100)*ethPrice)/100)/USDA_PRECISION;
}

function calculateHalfValue(uint256 amount) public pure returns(uint128){
        return uint128((amount * 50)/100);
}

Calculates the 50% of the deposited amount value with current ETH price, then 80% of the calculated amount is going to ABOND USDa pool to back ABOND.

Functions which are using the above logic

• Borrowing Withdraw.

Withdraw ETH calculation

borrowing.sol

uint128 ethToReturn;
//Calculate current depositedAmount value
uint128 depositedAmountvalue = (
    depositDetail.depositedAmount * depositDetail.ethPriceAtDeposit)/_ethPrice;

if(borrowingHealth > 10000){
    // If the ethPrice is higher than deposit ethPrice,call withdrawOption in options contract
    ethToReturn = (depositedAmountvalue + (options.calculateStrikePriceGains(depositDetail.depositedAmount,depositDetail.strikePrice,_ethPrice)));
    if(ethToReturn > depositDetail.depositedAmount){
        ethRemainingInWithdraw += (ethToReturn - depositDetail.depositedAmount);
        omniChainBorrowing.ethRemainingInWithdraw += (ethToReturn - depositDetail.depositedAmount);
    }else{
        ethRemainingInWithdraw += (depositDetail.depositedAmount - ethToReturn);
        omniChainBorrowing.ethRemainingInWithdraw += (depositDetail.depositedAmount - ethToReturn);
    }
    ethValueRemainingInWithdraw += (ethRemainingInWithdraw * _ethPrice);
    omniChainBorrowing.ethValueRemainingInWithdraw += (ethRemainingInWithdraw * _ethPrice);
}else if(borrowingHealth == 10000){
    ethToReturn = depositedAmountvalue;
}else if(8000 < borrowingHealth && borrowingHealth < 10000) {
    ethToReturn = depositDetail.depositedAmount;
}else{
    revert("BorrowingHealth is Low");
}

Calculate the withdraw amount by taking the ratio of deposit ETH price to current ETH price.

If the current ETH price is higher than deposited ETH price,

Cumulative rate calculation

BorrowLib.sol

function calculateCumulativeRate(
        uint128 noOfBorrowers,
        uint256 ratePerSec,
        uint128 lastEventTime,
        uint256 lastCumulativeRate
    )

Param Name	Type	Description
noOfBorrowers	uint128	Total number of borrowers in treasury.
ratePerSec	uint256	Interest rate per second.
lastEventTime	uint128	Timestamp of last event.
lastCumulativeRate	uint256	Previous cumulative rate.

Here, event represents Deposit, Withdraw and Liquidation.

BorrowLib.sol

currentCumulativeRate = lastCumulativeRate * _rpow(ratePerSec, timeInterval, RATE_PRECISION);
currentCumulativeRate = currentCumulativeRate / RATE_PRECISION;

Current cumulative rate = last cumulative rate * (rate per second) ^ time interval.

To calculate the current cumulative rate, multiply the previous cumulative rate with interest rate per second to the power of time interval between two events.

Functions which are using the above logic

• Borrowing Deposit.

• Borrowing Withdraw.

• Borrow Liquidation.

Calculation of ratio of CDS Pool value to ETH vault value

BorrowLib.sol

function calculateRatio(
        uint256 _amount,
        uint currentEthPrice,
        uint128 lastEthprice,
        uint128 noOfBorrowers,
        uint256 latestTotalCDSPool,
        IBorrowing.OmniChainBorrowingData memory previousData
)    

Param Name	Type	Description
_amount	uint256	ETH amount, the user is depositing.
currentEthPrice	uint256	Current ETH to USD price.
lastEthPrice	uint128	ETH price when the last event happened.
noOfBorrowers	uint128	Total number of borrowers in the protocol.
latestTotalCDSPool	uint256	Total CDS amount accumulated in the protocol.
previousData	Struct OmniChainBorrowingData	Previously stored global data of borrowing contract.

BorrowLib.sol

// Calculate net P/L of CDS Pool
netPLCdsPool = price difference between current and last ETH price * noOfBorrowers;
previousData.cdsPoolValue = previousData.totalCDSPool + netPLCdsPool;

Initially calculate the net P&L of CDS, if the current ETH price is higher than last ETH price , then its profit else its loss.

If the ratio calculation is for first deposit in the protocol, then calculate net CDS Pool value by adding netPLCdsPool with total CDS amount accumulated. else,

BorrowLib.sol

previousData.cdsPoolValue = previousData.cdsPoolValue + ( 
    latestTotalCDSPool - previousData.totalCDSPool) + netPLCdsPool;

Add the netPLCdsPool with previous net CDS Pool value and CDS amount deposited after last event.

BorrowLib.sol

ratio = currentCDSPoolValue / currentEthVaultValue;

Finally, calculate the ratio by dividing currentCDSPoolValue by currentEthVaultValue.

Functions which are using the above logic

• Borrowing Deposit.

• Borrowing Withdraw.

• CDS Withdraw.

Downside Calculation

BorrowLib.sol

function calculateDownsideProtected(
    uint128 amount,
    uint128 currentEthPrice,
    uint128 depositEthPrice
) public pure returns (uint128) {
    if (currentEthPrice < depositEthPrice) {
        return
            (amount * (depositEthPrice - currentEthPrice)) /
            (100 * USDA_PRECISION);
    } else {
        return 0;
    }
}

Calculates the downside needs to protect by CDS user.

Functions which are using the above logic

• Borrowing Withdraw.

Options fees per second Calculation

BorrowLib.sol

function calculateOptionsFeesPerSec(
    uint128 optionsFees
) public pure returns (uint128) {
    return (optionsFees * OPTIONS_FEES_PRECISION) / 30 days;
}

Calculates the options fees per second by dividing the options fees paid by user during deposit by number of seconds in 30 days.