PnL & Settlement

Audience: Traders and liquidity providers who want to understand how Twilight calculates, tracks, and settles profits and losses (PnL). Goal: Explain how trader positions generate BTC-denominated PnL, how settlement works, and how these flows impact pool value (NAV).

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1. Overview

Twilight uses an inverse BTC-USD perpetual model. All PnL, margin, and accounting are denominated in SATS (BTC units).

• Price feeds come from the external Binance spot mid-price (updated every 0.5 s).

• PnL is calculated in BTC, even though notional values are in USD.

• Settlement occurs atomically when a position closes manually or is liquidated.

• There is no streaming PnL — unrealized PnL is computed off-chain and applied only at close.

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2. PnL Model

Twilight’s PnL model follows standard inverse-perpetual math, expressed in BTC units.

Unrealized PnL

For long positions:

uPnL (BTC) = PositionSize × (1/EntryPrice - 1/ExitPrice)

For short positions:

uPnL (BTC) = PositionSize × (1/ExitPrice - 1/EntryPrice)

Where:

Variable	Meaning
PositionSize	Contract size in BTC (notional ÷ mark price).
EntryPrice	Price at which the position opened.
ExitPrice	Current oracle mark (for unrealized PnL) or close price (for realized PnL).

Positive PnL increases trader equity; negative PnL reduces it.

Since this is an inverse contract, price movements affect BTC collateral non-linearly as USD prices change.

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3. Position Lifecycle

Each position in Twilight is isolated — it has its own margin, leverage, and lifecycle.

Here’s how the system tracks and settles PnL:

1. Open:

   Trader posts margin → position notional and leverage calculated.

2. Hold:

   Unrealized PnL computed off-chain (via relayer) as price updates.

   Hourly funding adjustments accrue in memory.

3. Close (manual or liquidation):

   PnL realized, margin released or seized.

4. Settle:

   Pool NAV and trader account updated atomically at block level (verified via zkOS).

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4. Funding Integration

Hourly funding rate transfers are applied at the time of settlement.

These compensate the pool for directional skew (as explained in Fees & Funding).

skew_raw = (L_usd - S_usd) / (L_usd + S_usd)
rate_hr  = (skew_raw^2 / (ψ * 8)) * sign(skew_raw)

At position close:

• If funding was positive, longs pay and shorts receive.

• If funding was negative, shorts pay and longs receive.

• Any residual difference flows to Pool NAV, rewarding LPs.

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5. Settlement Mechanics

Settlement finalizes all economic transfers in one atomic block event.

For Traders

• PnL realized in BTC (SATS) using the oracle mark at close.

• Margin + PnL returned to the trader’s funding account.

• If position was liquidated, full margin is forfeited.

For the Pool (LPs)

• Losing positions: Margin and losses accrue to Pool NAV.

• Winning positions: Pool pays out trader PnL from its collateral.

• Funding + Fees: Always flow into the pool to offset trader profits.

Settlement is validated through zkOS proofs ensuring state correctness and privacy.

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6. Example Calculations

Example 1 – Long Position

A trader opens a 1 BTC long at $40 000, closes at $42 000:

PnL = 1 × (1/40000 - 1/42000)
PnL = +0.00000119 BTC  (≈ 119 SATS)

If the position had 50× leverage, the initial margin ≈ 0.02 BTC,

so the realized return is ~0.6 %.

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Example 2 – Short Position

A trader opens a 1 BTC short at $42 000, closes at $40 000:

PnL = 1 × (1/40000 - 1/42000)
PnL = +0.00000119 BTC  (≈ 119 SATS)

The same magnitude applies — direction determines sign.

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7. Pool Accounting & NAV Adjustments

After every settlement, the pool’s BTC balance is updated as:

Pool NAV = TVL - TTM + Σ(RealizedPnL + Funding + Fees)

Where:

Variable	Description
TVL	Total LP deposits.
TTM	Total trader margin locked.
RealizedPnL	Sum of all closed trade PnLs (positive or negative).
Funding / Fees	Hourly skew compensation and trading fees flowing to the pool.

This ensures pool solvency and LP transparency.

In the testnet, withdrawals are instantaneous and reflect updated NAV per block.

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8. Settlement Flow Diagram

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9. Quick Reference — PnL Signs & Effects

Action	Market Move	Trader Outcome	Pool Effect	Notes
Open Long	Price ↑	Trader profit (BTC gain)	Pool pays PnL	Funding rate may reduce bias
Open Long	Price ↓	Trader loss (BTC loss)	Pool collects margin + loss	—
Open Short	Price ↓	Trader profit (BTC gain)	Pool pays PnL	—
Open Short	Price ↑	Trader loss (BTC loss)	Pool collects margin + loss	—
Liquidation	Margin ≤ MM	Trader loses all margin	Pool absorbs PnL impact	Verified per block
Funding > 0	Long-heavy skew	Longs pay shorts / pool	LPs earn from skew	Applied hourly

10. Key Takeaways

• PnL is BTC-denominated — every trade result settles in SATS.

• Each position is independent and settles atomically on close.

• Funding and fees integrate seamlessly into final PnL.

• All accounting verified via zkOS proofs for on-chain integrity.

• Pool NAV automatically adjusts — keeping LP exposure accurate.

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