How Liquidation Auctions Repay Undercollateralized Loans
A liquidation auction on an undercollateralized loan does not raise the sum needed to repay the debt; it discovers the discount at which a bidder will take the collateral, and that discount decides how much of the debt gets repaid. Read the numbers — discount curve, debt-to-collateral ratio, gas — and they all state the same trade. The condition underneath: the curve, not a race, sets the price, so the auction can clear even when no bot would touch the position at market terms.
What the auction is for
Overcollateralized lending liquidates like a race: health factor crosses one, bots repay the debt and take the collateral at a fixed bonus, first transaction wins. That assumes the collateral covers the debt. An undercollateralized loan breaks the assumption, so no rational bot repays 100 to take 80. The lender calls the loan and a time-based liquidation auction opens; its discount is set by the pair contract, not by who clicks first. Fraxlend, Frax's lending protocol, runs undercollateralized pairs on this design.
How the repayment happens
The repayment happens in one step: a bidder repays part of the borrower's debt and receives collateral booked at a discount. Debt is 100, collateral books at 80. At a 5% discount, the bidder repays 76 and takes the collateral; the lender is repaid 76 and writes off the remaining 24. At a 10% discount the same collateral repays 72; at 20%, 64. The lender's recovery is always the collateral's book value times (1 − discount), capped by the debt, and the curve's position when the bid lands decides which number applies. If the auction ends with no bidder, the pair hands the collateral to the lender and the lender books the uncovered remainder as a loss. The pair's yield is the compensation for the auctions that end this way.
The same number reads three ways:
- Lender: recovery is collateral book value × (1 − discount), capped by the debt.
- Bidder: gross margin is the discount on the collateral, before gas, slippage and carry.
- Borrower: the residual debt is cancelled, and the discount is the exit price for a position that no longer covers itself.
What it costs
The bidder pays the real costs. The liquidation is a transaction on the Ethereum Network, so gas is a line item, not an afterthought; on a slow auction the choice between a cheaper gas price and settling at the current discount is the whole game. The collateral then has to be sold into a book thinner than the pair's mark price implies, and the price can move while you carry it. MetaMask Wallet is enough to run the workflow, with the Uniswap Protocol as the spot reference before you bid.
What decides the bid
Everything comes down to one comparison: current discount versus your all-in cost to exit the collateral. If the discount covers gas, slippage and carry, you bid; if not, you wait. The curve's slope tells you which way waiting cuts: a decaying discount puts the best terms at the open, so speed wins; a widening discount puts them at the close, where someone else is waiting. The pair's parameters set the start, floor and slope, so read the contract, not the UI.
For a Frax ecosystem asset, the live price to use in that comparison is the one quoted on Frax Swap.
The discount, read against an external price, is the single number that matters; the rest of the machinery only tells you how much of it you keep. An auction cannot create recovery the collateral does not have; it only decides who takes the missing piece.