Deposit for minting

Depositing collateral into the vault can mint both USB and margin tokens.

Figure: Mint Process

The V-Vault operates in two modes, starting initially with the stability mode, when the Vault's AAR deviates below the set lower limit (Safety AAR, AARS) or exceeds the upper limit (Upper AAR, AARU), the protocol enters an adjustment phase.

Taking the ETH vault as an example:

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Stability Mode

When assets are first deposited into the Vault for minting, as the quantities of existing USB and ETHx are zero, we calculate the minting ratio based on the initial price P_(eth-i) and then maintain this minting ratio unchanged throughout the stability phase. The protocol records the quantity of USB minted in each Vault, and the total supply of USB is the sum of USB minted across all Vaults.

When the contract is initially created, USB and ETHx are generated in a fixed ratio. The specific quantities and ratios are calculated using the following formula:

$\Delta USB = \Delta ETH \times P_{eth-i} \times \frac{1}{AART_{eth}}$

$\Delta ETHx = \Delta ETH \times \left(1 - \frac{1}{AART_{eth}}\right)$

Where:

• $\Delta USB$ : The quantity of minted USB.

• $\Delta ETHx$: The quantity of minted ETHx.

• $\Delta ETH$: The quantity of ETH used for minting.

• $P_{eth-i}$: The initial price of ETH relative to USD (provided by an oracle).

• $AART_{eth}$: The protocol's target AAR (Asset Adequacy Ratio) for the ETH vault.

After the initiation, when depositing into the ETH vault, users can mint USB and ETHx in a fixed ratio. The formulas for calculating the minted amounts are as follows:

$\Delta USB = \Delta ETH \times \frac{M_{USB-ETH}}{M_{ETH}}$

$\Delta ETHx = \frac{\Delta USB \times M_{ETHx}}{M_{USB-ETH}}$

Example：

We assume ( AART_{eth} = 150% ). When 2 ETH are first deposited into the Vault, and the real-time market price of ETH at that time is $2000, then:

$\Delta USB = \Delta ETH \times P_{eth-i} \times \frac{1}{AART_{eth}} = 2 \times 2000 \times 0.6667 = 2666.7;$

$\Delta ETHx = \Delta ETH \times \left(1 - \frac{1}{AART_{eth}}\right) = 2 \times 0.3333 = 0.6667$

If another user deposits 1 ETH into the Vault, assuming the market price of ETH is $2200, and the protocol is still in the stability phase, the user can obtain ( \Delta USB ) and ( \Delta ETHx ) as follows:

$\Delta USB = \Delta ETH \times \frac{M_{USB-ETH}}{M_{ETH}}=1 \times \frac{2666.7}{2}=1333.4$

$\Delta ETHx = \frac{\Delta USB \times M_{ETHx}}{M_{USB-ETH}} =\frac{1333.4 \times 0.6667}{2666.7}=0.3334$

In this scenario, with a total of 3 ETH in the Vault, the Vault has generated a total of 4000 USB and 1 ETHx.

From the examples provided above, we can observe that within the protocol's stability phase, the number of USB and ETHx generated for each ETH deposited remains constant.

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Adjustment Mode

When the Vault's AAR deviates below the set lower limit (Safety AAR, AARS) or exceeds the upper limit (Upper AAR, AARU), the protocol enters an adjustment phase. During this adjustment phase, the method of asset minting changes.

When AAR rises above AARU, users can mint USB individually. The corresponding minting formula is as follows:

$\Delta USB = \Delta ETH \times P_{eth}$

If users want to mint ETHx, they still need to mint USB+ETHx according to the protocol's calculated ratio.

When AAR falls below AARS, users can mint ETHx alone using the underlying asset. The minting formula in this case is:

$\Delta ETHx = \frac{\Delta ETH \times P_{eth} \times M_{ETHx}}{M_{ETH} \times P_{eth} - M_{USB-ETH}}$

When AAR further drops below 101%, the formula for minting ETHx alone will change to:

$\Delta ETHx = \frac{\Delta ETH \times P_{eth} \times M_{ETHx} \times 100}{M_{USB-ETH}}$

Where:

• $\Delta USB$ : The quantity of USB minted.

• $\Delta ETHx$: The quantity of ETHx minted.

• $\Delta ETH$: The quantity of ETH used for minting.

• $P_{eth}$: The real-time price of ETH relative to USD (provided by the oracle).

• $M_{ETH}$: The quantity of ETH in the Vault.

• $M_{ETHx}$: The quantity of ETHx minted in the ETH Vault.

• $M_{USB-ETH}$: The quantity of USB already minted in the ETH Vault.

If users want to mint USB, they still need to mint USB+ETHx according to the protocol's calculated ratio.

When Vault's AAR returns to AART, the protocol returns to the Stability Mode, and the asset minting formula reverts to the calculation used during the stability phase.