Liquidations

Partial Liquidations

Nectra employs partial liquidations to safeguard the system when a borrowing position's LTV reaches 90.9%. During such an event, nUSD is repaid to the system to reduce the outstanding debt, and a liquidation penalty is applied.

The liquidator earns a share of this penalty, capped at $10 worth of cBTC, while the remainder of the fee is paid to the Savings Account module.

Calculating nUSD Required to Fix LTV

The nUSD required to pay for the liquidation can be provided from several sources and is calculated using the following formulas:

$$\text{nUSDtoFixLTV} = \frac{\text{Debt} \times \text{IR} - \text{Collateral} \times \text{Price}}{\text{IR} - 100\%}$$

Where:

• nUSDtoFixLTV represents the nUSD required to adjust the position's LTV to the maximum LTV.

• Debt is the current amount of nUSD borrowed by the user.

• IR denotes the issuance ratio, the target LTV expressed as a percentage, for example, 83.3%.

• Collateral refers to the amount of cBTC that has been deposited as collateral.

• Price indicates the current market price of cBTC.

Calculating Liquidation Penalty in nUSD

$$\text{PenaltynUSD} = \text{nUSDtoFixLTV} \times \text{Penalty}$$

Where:

• PenaltynUSD represents the additional debt that will be burned from the account to cover the liquidation penalty.

• Penalty refers to the liquidation penalty, currently set to 15%.

Calculating Total Liquidation Cost

$$\text{LiquidationCost} = \text{nUSDtoFixLTV + PenaltynUSD}$$

Liquidation Cost represents the total nUSD required by a liquidator. The total collateral reward for a given liquidation is calculated as:

$$\text{PenaltycBTC} = \frac{\text{PenaltynUSD} \times \text{IR}}{\text{Price}}$$

The resulting cBTC penalty is divided into two parts when a liquidation occurs. 10% of the penalty is directed to the Savings Account module, and up to $10 worth of the 90% share is allocated to the liquidator. Any amount exceeding $10 will be sent to the Savings Account module.

Liquidation Functions

Nectra offers several options for partial liquidations.

Savings Account Module Liquidations

The Savings Account module can source nUSD from:

• Flash minting

• Idle nUSD deposited into the Savings Account

• Temporarily withdrawing nUSD from Savings Account yield generation strategies

After the liquidation, the underlying collateral is sold to return the system to its original state, in addition to the fees received. The liquidation penalty is earned by the Savings Account Module. The cBTC reward received by the liquidator can be calculated as:

Public Liquidations

Individuals can use their nUSD (or nUSD acquired through other sources) to perform liquidations. Users receive an equivalent amount of cBTC and a share of the liquidation penalty. The amount of cBTC received from a self-funded liquidation can be calculated using:

$$\text{cBTCReceived} = \frac{ \text{nUSDtoFixLTV}}{\text{Price}} + \text{PenaltycBTC} \times 90\%$$

While the liquidator will be fully reimbursed for their nUSD in the form of cBTC, the value of the cBTC reward they receive from the penalty cBTC is capped at $10.

Flash and Liquidate

The "flash mint" function allows users to perform public liquidations without having the required nUSD. The acquired cBTC is then swapped for nUSD through a DEX to repay the borrowed amount. The liquidator's reward is a portion of the liquidation penalty, minus any DEX fees, slippage incurred during the cBTC-to-nUSD swap, and the flash mint fee. The remaining portion of the penalty is allocated to the Savings Account module. The liquidator's reward is calculated as:

$$\text{cBTCReceived} = \text{PenaltycBTC}\times 90\%-\text{SwapLoss}-\text{FlashFee}$$

Socialized Liquidations

As a last resort, if a position approaches the point of going underwater (95.2% LTV), its debt and collateral can be proportionally distributed to other positions in the system based on their existing debt.

This debt-share distribution helps prevent cascading liquidation issues. Before redistribution, a fixed value reward of 10 nUSD is added to the liquidated positions’ debt and rewarded to the caller.