Margin Calculations

Diffusal uses a SPAN-like portfolio margin system that calculates margin requirements by stress testing positions across multiple market scenarios. This approach captures the worst-case loss across plausible market movements.

For Black-Scholes pricing used in these calculations, see Black-Scholes Model.

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Stress Testing

4 Corner Scenarios

The margin engine tests each portfolio against four extreme market scenarios combining ±30% spot moves with +50%/−30% IV changes. These scenarios capture the most adverse combinations of price and volatility movements for option portfolios.

See Margin System: Stress Scenarios for the complete scenario table and rationale.

Stressed Price Calculation

For each scenario, option prices are recalculated using Black-Scholes with stressed parameters:

$$S_{\text{stressed}} = S \times \text{spotMultiplier}$$ $$\sigma_{\text{stressed}} = \sigma \times \text{ivMultiplier}$$

The stressed option price is then computed:

$$P_{\text{stressed}} = \text{BlackScholes}(S_{\text{stressed}}, K, r, \sigma_{\text{stressed}}, T)$$

Scenario Loss

For each scenario, the portfolio loss is calculated by comparing current mark prices to stressed prices:

$$\text{Scenario Loss} = \sum_{i=1}^{n} (P_{\text{mark},i} - P_{\text{stressed},i}) \times \text{size}_i$$

Where:

• n = number of positions
• P_mark = current Black-Scholes price
• P_stressed = price under stress scenario
• size = position size (positive for long, negative for short)

Maximum Stress Loss

The stress loss component of margin is the maximum loss across all four scenarios:

$$\text{Stress Loss} = \max_{s \in \{1,2,3,4\}} |\text{Scenario Loss}_s|$$

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Margin Requirements

Initial Margin (IM)

Initial margin is the collateral required to open or maintain positions:

$$\text{IM} = \text{Stress Loss} + \text{Adverse PnL Buffer} + \text{Notional Buffer}$$

Components:

1. Stress Loss - Maximum loss across 4 corner scenarios

2. Adverse PnL Buffer - Additional buffer when positions are underwater:

$$\text{Adverse PnL Buffer} = \max(0, -\text{unrealizedPnL}) \times 1.05$$

3. Notional Buffer - Percentage of total notional exposure:

$$\text{Notional Buffer} = \text{Total Notional} \times 0.15$$

Maintenance Margin (MM)

Maintenance margin is the minimum collateral to avoid liquidation:

$$\text{MM} = \text{IM} \times 0.80$$

A position becomes liquidatable when equity falls below maintenance margin.

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Unrealized PnL

Unrealized profit/loss across all positions:

$$\text{PnL} = \sum_{i=1}^{n} (P_{\text{mark},i} - P_{\text{entry},i}) \times \text{size}_i$$

Where:

• P_mark = current Black-Scholes price
• P_entry = price at which position was opened
• size = signed position size

For long positions (size > 0): profit when mark > entry For short positions (size < 0): profit when mark < entry

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Total Notional

Total notional exposure of the portfolio:

$$\text{Notional} = \sum_{i=1}^{n} |\text{size}_i| \times S_i$$

Where:

• size = position size
• S = current spot price of the underlying

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Equity and Health

Equity

$$\text{Equity} = \text{Deposit} + \text{Unrealized PnL}$$

Health Check

A user is healthy when:

$$\text{Equity} \geq \text{MM}$$

A user is liquidatable when:

$$\text{Equity} < \text{MM}$$

Maximum Withdrawal

$$\text{Max Withdraw} = \max(0, \text{Equity} - \text{IM})$$

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Constants Reference

All margin constants are defined in Constants.sol:

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Contract Interface

MarginEngine Functions

• calculateInitialMargin(positions, quoterAddress) — Calculate IM for an array of positions (returns WAD)
• calculateMargin(positions, quoterAddress) — Get complete margin metrics: unrealizedPnL (WAD, can be negative), stressLoss (WAD), initialMargin (WAD), maintenanceMargin (WAD)

CollateralVault Functions

• getMarginInfo(user) — Returns complete MarginInfo struct containing: deposit (USDC), unrealizedPnL, equity (deposit + unrealizedPnL), initialMargin, maintenanceMargin, maxWithdraw, and isHealthy (whether equity >= MM)

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Implementation

The margin calculations are implemented in Solidity:

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Related

• Margin System — Protocol-level margin system with worked examples
• Black-Scholes Model — Option pricing formulas used in stress calculations
• Solidity Math — Precision handling and numeric conversions
• Liquidation — What happens when equity falls below MM