Liquidation & Auto-Deleveraging (ADL)

This document describes how the perpetual futures exchange protects itself from under-collateralised accounts and socialises losses via auto-deleveraging and the insurance fund.

1. Liquidation trigger

Every account has an equity and a maintenance margin (MM):

$equity = collateralValue + \sum unrealisedPnl - \sum accruedFunding$

$MM = \sum ∣ positionSize ∣ \times oraclePrice \times mmr$

where $mmr$ is the per-pair maintenance-margin ratio. An account becomes liquidatable when

$equity < MM$

Strict inequality: an account whose equity exactly equals its MM is still safe. An account with no open positions is never liquidatable regardless of its equity.

2. Close schedule

When an account is liquidatable, the system computes the minimum set of position closures needed to restore it above maintenance margin.

For every open position, compute its MM contribution:

$mmContribution = ∣ size ∣ \times oraclePrice \times mmr$
Sort positions by MM contribution descending (largest first).
Walk the sorted list and close just enough to cover the deficit:
- $deficit = MM - equity$
- For each position:
  - If $deficit \leq 0$ : stop
  - $closeSize = min (⌈ \frac{deficit}{oraclePrice \times mmr} ⌉, ∣ size ∣)$
  - $deficit - = closeSize \times oraclePrice \times mmr$

This produces a vector of $(pairId, closeSize)$ entries. Each $closeSize$ has the opposite sign of the existing position (a long is closed with a sell, a short with a buy). Only positions that contribute to the deficit are touched and they may be partially closed when the deficit is small relative to the position.

3. Position closure

Each entry in the close schedule is executed in two phases:

3a. Order book matching

The close is submitted as a market order against the on-chain order book. It matches resting limit orders at price-time priority. Any filled amount is settled normally (mark-to-market PnL between the entry price and the fill price).

3b. Auto-deleveraging (ADL)

If any quantity remains unfilled after the order book is exhausted, the system automatically deleverages against counter-parties. The unfilled remainder is closed against the most profitable counter-positions at the liquidated user’s bankruptcy price.

Counter-party selection: Positions are indexed by the tuple $(pairId, entryPrice, user)$ . For a long being liquidated (selling), the system finds shorts with the highest entry price (most profitable) first. For a short being liquidated (buying), it finds longs with the lowest entry price first.¹

Bankruptcy price: The fill price at which the liquidated user’s total equity would be exactly zero:

$bp = oraclePrice - \frac{equity}{closeAmount} (for longs)$

$bp = oraclePrice + \frac{equity}{closeAmount} (for shorts)$

Since equity is typically negative for liquidatable users, the bankruptcy price is worse than the oracle price — the counter-party receives a favourable fill. The counter-party’s resting limit orders are not affected by ADL; only their position is force-reduced.

Liquidation fills (both order-book and ADL) carry zero trading fees for both taker and maker.

4. Liquidation fee

After all positions in the schedule are closed, a one-time liquidation fee is charged:

$rawFee = closedNotional \times liquidationFeeRate$

$remainingMargin = max (0, margin + userPnlAfterCloses)$

$fee = min (rawFee, remainingMargin)$

The fee is deducted from the user’s margin and routed to the insurance fund (not the vault). It is capped at the remaining margin so the fee itself never creates bad debt.

5. PnL settlement

All PnL from the liquidation fills (user, book makers, ADL counter-parties) is settled atomically as in-place USD margin adjustments — no token transfers occur. Both user and maker PnL are applied via the same settlement logic described in Order matching §8.

6. Bad debt

After PnL and fee settlement, if the user’s margin is negative the absolute value is bad debt. The margin is floored to zero and the bad debt is subtracted from the insurance fund:

$badDebt = ∣ min (0, margin after settlement) ∣$

$user.margin \leftarrow 0$

$insuranceFund - = badDebt$

The insurance fund may go negative. A negative insurance fund represents unresolved bad debt — future liquidation fees will replenish it.

Note: when positions are fully ADL’d at the bankruptcy price, the user’s equity is zeroed by construction. Bad debt from ADL fills is therefore zero. Bad debt arises only from book fills at prices worse than the bankruptcy price (e.g., thin order books with deep bids/asks far from oracle).

7. Insurance fund

The insurance fund is a separate pool from the vault that absorbs bad debt and is funded by liquidation fees.

Funding: Every liquidation fee (§4) is credited to the insurance fund.

Usage: Every bad debt event (§6) is debited from the insurance fund.

Negative balance: The insurance fund may go negative when accumulated bad debt exceeds accumulated fees. This is the simplest approach — no special trigger or intervention is needed. Future liquidation fees will naturally replenish the fund.

The vault’s margin is never touched for bad debt or liquidation fees. This isolates liquidity providers from liquidation losses.

Examples

All examples use:

Parameter	Value
Pair	BTC / USD
Maintenance-margin ratio (mmr)	5 %
Liquidation-fee rate	0.1 %
Settlement currency	USDC at $1

Example 1 — Clean liquidation on book (no bad debt)

Setup

	Alice	Bob (maker)
Direction	Long 1 BTC	Bid 1 BTC @ $47,500
Entry price	$50,000	—
Margin	$3,000	$10,000

BTC drops to $47,500

Alice’s account

$equity = $3, 000 + 1 \times ($47, 500 - $50, 000) = $3, 000 - $2, 500 = $500$

$MM = 1 \times $47, 500 \times 5% = $2, 375$

$$500 < $2, 375 \Rightarrow liquidatable$

Close schedule

Alice has one position; the full 1 BTC long is scheduled for closure.

Execution

The long is closed (sold) into Bob’s resting bid at $47,500.

$AlicePnL = 1 \times ($47, 500 - $50, 000) = - $2, 500$

Liquidation fee

$closedNotional = 1 \times $47, 500 = $47, 500$

$rawFee = $47, 500 \times 0.1% = $47.50$

$remainingMargin = max (0, $3, 000 - $2, 500) = $500$

$fee = min ($47.50, $500) = $47.50$

Settlement (margin arithmetic)

Alice’s margin starts at $3,000.

$margin - = $47.50 (fee) \Rightarrow $2, 952.50$

$margin + = (- $2, 500) (PnL) \Rightarrow $452.50$

Final margin is positive — no bad debt.

$insuranceFund + = $47.50 (fee revenue)$

Example 2 — ADL at bankruptcy price (no book liquidity)

Setup

	Charlie	Dana
Direction	Long 1 BTC	Short 1 BTC
Entry price	$50,000	$55,000
Margin	$3,000	$10,000

BTC drops to $46,000

Charlie’s account

$equity = $3, 000 + 1 \times ($46, 000 - $50, 000) = $3, 000 - $4, 000 = - $1, 000$

$MM = 1 \times $46, 000 \times 5% = $2, 300$

$- $1, 000 < $2, 300 \Rightarrow liquidatable$

Close schedule

Charlie’s full 1 BTC long is scheduled for closure.

Order book matching

No bids on the book — the full 1 BTC is unfilled.

ADL

Bankruptcy price for Charlie’s long:

$bp = $46, 000 - \frac{- $1 , 000}{1} = $46, 000 + $1, 000 = $47, 000$

Dana holds the most profitable short (entry $55,000, current oracle $46,000). Her position is force-closed at $47,000.

Charlie’s PnL at bankruptcy price:

$CharliePnL = 1 \times ($47, 000 - $50, 000) = - $3, 000$

$margin : $3, 000 + (- $3, 000) = $0 (zeroed by construction)$

Dana’s PnL at bankruptcy price:

$DanaPnL = - 1 \times ($47, 000 - $55, 000) = $8, 000$

$DanaMargin : $10, 000 + $8, 000 = $18, 000$

Liquidation fee

$remainingMargin = max (0, $3, 000 - $3, 000) = $0$

$fee = $0 (no margin left)$

No bad debt, no insurance fund impact. Dana receives the full PnL at the bankruptcy price, which is better than the oracle price for her.

Final state

	Balance
Charlie	$0 (fully liquidated)
Dana	$18,000 (profit at bp)
Insurance fund	unchanged

Example 3 — Book fill creates bad debt

Setup

	Charlie	Bob (maker)
Direction	Long 1 BTC	Bid 1 BTC @ $46,000
Entry price	$50,000	—
Margin	$3,000	$50,000
Insurance fund	$500

BTC drops to $46,000

Charlie’s liquidation

Same equity and MM as Example 2. Liquidatable.

Order book matching

The bid at $46,000 fills Charlie’s full 1 BTC sell.

$CharliePnL = 1 \times ($46, 000 - $50, 000) = - $4, 000$

Liquidation fee

$remainingMargin = max (0, $3, 000 - $4, 000) = $0$

$fee = $0$

Bad debt

Charlie’s margin after PnL: $$3, 000 - $4, 000 = - $1, 000$ .

$badDebt = $1, 000, margin \leftarrow $0$

$insuranceFund : $500 - $1, 000 = - $500$

The insurance fund goes negative. Future liquidation fees will replenish it.

Final state

	Balance
Charlie	$0 (fully liquidated)
Insurance fund	−$500 (unresolved bad debt)
Vault	unchanged (isolated from losses)

This does not perfectly rank by total PnL since it ignores accumulated funding fees, but is a reasonable and efficient approximation. ↩

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