# Liquidation

If a user breaches their max LTV or if their health factor drops below 1, they will become eligible for liquidation. When a user gets liquidated, the liquidator can purchase 40% or more of their collateral at a discount. 

For example, consider a user who has borrowed 1,000 USDC against 1 ETH worth 2,000 USDC for an LTV of 50%. Assume the max LTV is 75% and the liquidation discount is 5%. Here's what will happen if the ETH price falls to 1,300 USDC.

```
// Pre-liquidation

Debt: 1,000 USDC
Collateral: 1 ETH
ETH/USDC price: 1,300 USDC
LTV = 1,000 / 1,300 = 0.769

// Liquidation

Liquidation discount: 6%
Collateral purchased: 0.4 ETH
ETH/USDC purchase price = 1,300 * (1 - 0.06) = 1,222 USDC
USDC liquidation amount = 1,222 * 0.4 = 488.8 USDC
Liquidator profit = 0.4 ETH * 1,300 USDC * 6% = 31.2 USDC

// Post-liquidation

Debt: 1,000 USDC - 488.8 USDC = 511.2 USDC
Collateral: 1 ETH - 0.4 ETH = 0.6 ETH
ETH/USDC price: 1,300 USDC
LTV = 511.2 / 780 = 0.655
```

In this example, the liquidated account is returned to a healthy LTV of 0.655 and the liquidator earns a profit of 31.2 USDC.

## Liquidation discount

The size of the liquidation discount is the sum of two parts:

1. **The exchange rate discount**. This discount depends on what currency the user is borrowing and what currency they're using as collateral. This discount is larger for volatile pairs and smaller for stable pairs.
2. **The collateral asset type discount**. This discount depends on whether the user is holding their collateral as prime cash, nTokens, or fCash. For prime cash, this discount is 0%. But for nTokens and fCash it will be positive and vary by currency.

$$
liquidation Discount = exchangeRateDiscount + collateralAssetTypeDiscount
$$

### Exchange rate discount

Each currency has its own liquidation discount. For example, the ETH liquidation discount is 6% and the USDC liquidation discount is 4%. The discount that will be used in liquidation is the greater of the collateral asset discount and debt asset discount.

$$
exchangeRateDiscount = max(collateral.discount, debt.discount)
$$

### Collateral asset type discount

* **Prime cash**: zero additional discount.
* **fCash**: fCash collateral asset type discounts work similarly to [fCash haircuts](https://docs.notional.finance/notional-v2/loan-to-value-ltv/local-currency-risk-factors#fcash). They are not flat percentages - they are discounts based on adjustments to the oracle rate. This means that liquidation discounts vary in size depending on the time to maturity of the fCash asset.
* **nTokens**: nTokens have a flat discount percentage that varies by currency. For example, nETH has a 2% collateral asset type discount.

### Example calculations

Here are some example liquidation discount calculations for users with different portfolios.

**Example 1: prime ETH collateral vs. fUSDC debt**

```
Collateral currency: ETH
Debt currency: USDC
Collateral asset type: prime cash

ETH discount: 6%
USDC discount: 4%
Prime cash discount: 0%

Liquidation discount = max(4%, 6%) + 0% = 6%
```

#### Example 2: fETH collateral vs. fUSDC debt

```
Collateral currency: ETH
Debt currency: USDC
Collateral asset type: fETH
fETH time to maturity: 0.5 years
fETH liquidation haircut: 1%
fETH discount ~= 0.5%

ETH discount: 6%
USDC discount: 4%
fETH discount: 0.5%

Liquidation discount = max(4%, 6%) + 0.5% = 6.5%
```

#### Example 3: nETH collateral vs. fUSDC debt

```
Collateral currency: ETH
Debt currency: USDC
Collateral asset type: nETH

ETH discount: 6%
USDC discount: 4%
nETH discount: 2%

Liquidation discount = max(4%, 6%) + 2% = 8%
```

### Single-currency liquidation discounts

Some accounts have debts that are in the same currency as their collateral. For example, a user might have a prime USDC debt against nUSDC collateral. In these scenarios, the liquidators will not receive an exchange rate discount. 

This means that the only liquidation discount for single-currency liquidations is the collateral asset type discount. 

#### Example: nUSDC collateral vs. Prime USDC debt

```
Collateral currency: USDC
Debt currency: USDC
Collateral asset type: nUSDC

nUSDC discount: 3%

Liquidation discount = 0% + 3% = 3%
```