S-Vault

The minting and redemption mechanism for the S-Vault is different because the price volatility of the stablecoin is low, so its mechanism is simpler compared to V-Vaults. Simply put, USB and xToken can mostly be minted and redeemed independently.

Taking the USDB vault as an example:

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Deposit for minting

When the contract is initially created or when the supply of USDBx is zero, USB cannot be minted directly. The first time USDB assets are deposited into the contract to mint USDBx, we preset the initial minting amount with the formula:

$\Delta USDBx = \Delta USDB$

After the initiation, when depositing into the USDB vault, users can mint USB or USDBx independently. The formulas for calculating the minted amounts are as follows:

$\Delta USB = \Delta USDB \times P_{usdb}$

$\Delta USDBx = \frac{\Delta USDB \times P_{usdb} \times M_{USDBx}}{M_{usdb} \times P_{usdb} - M_{USB-USDB}}$

Where:

• $\Delta USB$: The amount of USB minted

• $\Delta USDBx$: The amount of USDBx minted

• $\Delta USDB$: The amount of USDB deposited

• $P_{usdb}$: The price of USDB in terms of USD (assumed to be stable)

• $M_{usdb}$: The total amount of USDB in the vault

• $M_{USDBx}$: The total amount of USDBx minted

• $M_{USB-USDB}$: The amount of USB minted from the USDB vault

When the AAR falls below AARS, USB can no longer be minted independently. If users need to mint USB, USDBx will be minted at the same time in proportion, according to the following formula:

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

$\Delta USDBx = \frac{\Delta USB \times M_{USDBx}}{M_{USB-USDB}}$

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

$\Delta USDBx = \frac{\Delta USDB \times P_{usdb} \times M_{USDBx} \times 100}{M_{USB-USDB}}$

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Withdraw for redemption

When redeeming USDB using USB, the formulas based on the Asset Adequacy Ratio (AAR) are as follows:

$\Delta USDB = \frac{\Delta USB}{P_{usdb}} \quad \text{if AAR} ≥ 100\%$

$\Delta USDB = \frac{\Delta USB \times M_{USDB}}{M_{USB-USDB}}\quad \text{if AAR} < 100\%$

Where:

• $\Delta USB$: The amount of USB being redeemed

• $\Delta USDB$: The amount of USDB to be received

• $P_{usdb}$: The price of USDB

• $AAR$: The Asset Adequacy Ratio of the USDB vault

• $M_{USDB}$: The total amount of USDB in the vault

• $M_{USB-USDB}$: The amount of USB minted from the USDB vault

When redeeming USDB using USDBx, the calculation formula is as follows:

$\Delta USDB =\frac{M_{usdb} \times \Delta USDBx}{M_{USDBx}}- \frac{M_{USB-USDB} \times \Delta USDBx}{M_{USDBx} \times P_{usdb}}$

When the AAR falls below AARS, USDBx assets can no longer be redeemed for USDB independently. Users will need a certain amount of USB to match the proportion of the two assets before they can redeem USDB. For example, if a user wishes to redeem a quantity of USDBx, denoted as ∆USDBx, they will need to pair it with a corresponding amount of USB, denoted as ∆USB. The calculation formula is as follows:

$\Delta USB = \frac{\Delta USDBx \times M_{USB-USDB}}{M_{USDBx}}$

The amount of USDB redeemed with the paired ( \Delta USDBx ) and ( \Delta USB ) is:

$\Delta USDB = \frac{\Delta USDBx \times M_{USDB}}{M_{USDBx}}$

The redemption fee is 0.5%