Close Factor

Understanding the parameter that determines the liquidation threshold for undercollateralized positions

The Close Factor

• Is a parameter that determines the liquidation price, which is the price at which a borrower's position will be automatically liquidated if they fail to meet their “margin call”.

• Represents the maximum percentage of the borrower's collateral that can be liquidated (i.e. maximum amount of a borrower's current borrowed value that can currently be repaid in a single liquidate transaction), in the event of a default.

Calculation

Close Factor determines the portion of a borrower’s position that can be liquidated in a single event.

Mathematically, the Close Factor is

• A percentage that is multiplied by the value of the borrower's debt to determine the maximum amount that can be liquidated.

• A number that scales linearly between Minimum Close Factor and 1.0, reaching its maximum when the Borrowed Value has reached a critical value ("Critical Borrowed Value") between Liquidation Threshold to Collateral Value i.e. passed Complete Liquidation Threshold.

Minimum Close Factor is Close Factor at Liquidation Threshold.

On Carbon, the Minimum Close Factor is a parameter set to 0.1 that can be adjusted through Carbon governance. This means that 10% of the borrower position can be liquidated when the Borrowed Value passes the 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; 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.

On Carbon, the Liquidation Threshold (varies by asset) and Complete Liquidation Threshold (set to 0.7 on the protocol) are parameters that can be adjusted through Carbon governance.

Linear Scale

Close Factor is zero for borrowers that are not eligible for liquidation, i.e. Borrowed Value < Liquidation Threshold.

On the opposite spectrum, 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.

If Close Factor =

• 0.5, the borrower's position will be liquidated once the price falls to a level where half of the position's value has been sold to repay the lender.

• 0.8, the borrower's position will be liquidated once the price falls to a level where 80% of the position's value has been sold.

In summary, the close factor is a crucial parameter used to manage risk in lending by limiting the amount of position liquidated in a single transaction.