Partial Liquidations
Overview
In the event of liquidation, not all of the user's collateral may always be liquidated. The maximum amount of collateral that can be liquidated (and therefore repaid debt is determined by:
Health Factor: The collateralization level of the borrower's position (i.e. ratio of the value of the collateral to the outstanding debt)
Close Factor: The maximum percentage of the borrower's collateral that can be liquidated in the event of default.
Calculation
To determine the maximum collateral that can be liquidated, we must first find the Close Factor of the position.
Close Factor
Mathematically, the Close Factor is a number that scales linearly between a Minimum Close Factor (e.g. 0.1) and 1.0. The maximum value of 1.0 is reached when the Borrowed Value has reached a critical value ("Critical Borrowed Value"), which is between between initial Liquidation Threshold and the Collateral Value. This means that the position has passed its Complete Liquidation Threshold.
The Critical Borrowed Value is defined as:
B = LT + (CV-LT) * CLT, where
B = Critical Borrowed Value;
CV = Collateral Value;
LT = Liquidation Threshold;
CLT = Complete Liquidation Threshold; the CLT determines how far between LT and CV a borrower’s borrowed value must have progressed in order to allow a full liquidation. For example, 0.3 indicates 30% of the way from LT to CV.
There is a special case where Close Factor is always 1.0 if the Borrowed Value is less than the Small Liquidation Size, as long as the borrower is eligible for liquidation, so that small underwater positions can be easily completely removed.
Liquidation Amount
The Close Factor is then multiplied by the value of the borrower's collateral to determine the maximum amount of collateral that can be liquidated.
Example
Suppose:
Loan to Value (LTV) = 85% or 0.85;
Liquidation Threshold = 88% or 0.88;
Liquidation Bonus = 5% or 0.05;
Liquidation Bonus Fee = 10% or 0.10;
Minimum Close Factor = 0.10;
Close Factor = Variable factor; The close factor determines the percentage of the borrower's collateral that can be liquidated.
A borrower provides $100,000 in USDC and borrows $85,000 in ATOM (max LTV).
Collateral
$100,000 in USDC
Borrowings
$85,000 in ATOM
Loan to Value (LTV)
85% < Liquidation Threshold
Health Factor
= (Collateral Value * Liquidation Threshold) / Borrow Value
= (100,000 * 0.88) / 85,000
= 1.03529
> 1
The value of the borrowed ATOM increases to $92,500, bringing the user’s LTV ratio to 95.2% (thus exceeding the Liquidation Threshold of 88%).
Collateral
$100,000 in USDC
Borrowings
$92,500 in ATOM
Loan to Value (LTV)
92.5% > Liquidation Threshold
Health Factor
= (Collateral Value * Liquidation Threshold) / Borrow Value
= (100,000 * 0.88) / 92,000
= 0.95652
< 1
The borrower will be liquidated in order to ensure their position remains over-collateralized.
The exact calculation is as follows:
Find Close Factor
Critical Borrowed Value (B)
= LT + (CV-LT) * CLT
= $88,000 + ($100,000 - $88,000) * 0.7
= $96,400
Close Factor = 1 when Borrowed Value hits the critical amount of $96,400.
Close Factor (CF)
= (Debt - LT) / (CV - LT) * (1 - Minimum CF) + Minimum CF
= (92,500 - 88,000) / (100,000-88,000) * (1-0.1) + 0.1
= 0.4375
Calculate Maximum Liquidation Amount
Maximum amount that can be liquidated
= Close Factor * Debt (i.e. Current value of borrowings in USD)
= 0.4375 * $92,500
= $40468.75
The maximum amount that can be liquidated is $40468.75. The liquidator can initiate a liquidation and sell up to $40468.75 in collateral to repay the outstanding debt.
In return, the liquidator should expect to receive $40,468.75 * 1.045 = $42289.84 worth of the collateral after repaying the debt.
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