🏦Borrowing

Borrower Operations in Satoshi Protocol

The Satoshi Protocol provides users to access liquidity by depositing collateral, enabling them to borrow up to 90.91% of the collateral's value in SAT stablecoins (Loan-to-Value, LTV = 90.91%). This ensures that a Minimum Collateral Ratio (MCR) of 110% is maintained. Borrowers are granted the flexibility to repay their debt, borrow additional SAT, or withdraw some of their collateral, provided they consistently uphold the MCR. To ensure the stability of the system, the protocol enforces a minimum debt requirement of 12 SAT.

Borrowing Costs

When users mint SAT by borrowing against their collateral, the Satoshi Protocol imposes a minting fee and a fixed annual interest fee.

Additionally, an reserve of 2 SAT is set aside for gas compensation, which is added to the total debt. This reserve is intended to cover potential costs associated with the liquidation process. If the Position remains unliquidated, this 2 SAT gas fee reserve is returned to the borrower upon closing the Position. Conversely, if the Position undergoes liquidation, the reserved 2 SAT is awarded to the liquidator as compensation for the gas fees incurred during the liquidation process.

$$TotalBorrowing Fee=MintingFee + InterestFee + Gas Compensation$$

While the annual interest fee is fixed, the one-time minting fee is calculated as "base rate + 0.5%" and is applied to the total amount of SAT borrowed.

$$Minting Fee_t = BaseRate_t + 0.5 \%$$

The current base rate is determined by previous base rate and the quantity of SAT redeemed as a proportion of the total stablecoin supply. This dynamic fee structure has a minimum of 0.5% and a maximum cap of 5%, ensuring flexibility based on market conditions.

$$BaseRate_t = BaseRate_{t−1} + 0.5 × \frac{m}{n}$$

where $m$ denotes the amount of redeemed SAT, $n$ signifies the current supply of SAT.

Over time, the base rate experiences decay due to a decay factor applied with every SAT redemption and issuance before calculating the resulting fee. The decay follows the form:

$$BaseRate_t = BaseRate_{t−1} × δ^{∆t}$$

Where δ represents an hourly decay factor (0.944 in our case), and ∆t denotes the time elapsed in hours since the last redemption or loan issuance. The decay factor δ is selected to ensure a 12-hour half-life for the base rate.

Example: If the base rate is set at 0.5% and a user deposits BTC worth $2,000 to mint 2,000 SAT, they will incur a 0.5% one-time minting fee, amounting to 10 SAT, and an additional 2 SAT for gas compensation. Consequently, while the user receives 2,000 SAT, their total debt is 2,012 SAT. To fully close the Position and retrieve their BTC collateral, the borrower must settle this 2,012 SAT debt.

Restrictions During Recovery Mode

Borrowing operations within the Satoshi Protocol are subject to specific limitations when the system enters Recovery Mode. These restrictions are implemented to protect borrowers from potential liquidation risks that may arise due to fluctuations in the collateral price. To mitigate these risks, borrowers are advised to maintain a buffer between their current collateral ratio and the Minimum Collateral Ratio (MCR). In Recovery Mode, even Positions with higher collateral ratios (up to 150%) may be subject to liquidation. Consequently, borrowers aiming to minimize risk should ensure their Positions are sufficiently over-collateralized, when the protocol is approaching Recovery Mode. This strategy decreases the likelihood of liquidation and reduces the potential impact of large redemptions on their positions.

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Borrow Interest Rate

The Borrow Interest Rate in the Satoshi Protocol is free now when BTC is used as collateral. This interest accrues over time on the outstanding debt, serving as a crucial revenue stream for the protocol. For future collateral types, different interest rates will be applied.

Detailed Interest Amount Calculation

Interest accrues on the borrowed SAT for all borrowers within the protocol. The accumulation of interest is triggered by any interaction with the smart contracts, ensuring that the debt value remains up-to-date with the accrued interest over time.

Example of Interest Accrual

• Alice borrows 10,000 SAT against her BTC collateral.

• The annual interest rate is fixed, which translates to about debt amount times $1.427 × 10^{-9}$ per second.

• If there is no interaction with the smart contract for 100 seconds, interest continues to accrue on Alice's borrowed amount during this period.

• Upon a subsequent interaction with the protocol (e.g., Bob borrows some SAT), Alice's debt would reflect the accrued interest over those 100 seconds.

Using the specific per second interest rate

• The additional interest accrued over 100 seconds on Alice's initial borrowing of 10,000 SAT would be $10,000×1.427×10^{-9}=0.0001427$ SAT.

• Alice’s updated debt would be $10,000+0.0001427=10,000.0001427$ SAT after 100 seconds of accrued interest. For the next updated debt calculation, it would based on this amount of 10,000.0001427 SAT.