Options Portfolio Margining

Introduction

This document provides a comprehensive technical overview of the Options Portfolio Margining System, describing its methodology, margin calculations and risk management strategies.

Portfolio margining is a risk-based margin methodology that determines margin requirements based on the overall risk of a portfolio, rather than on predefined strategies. This approach aims to align margin requirements more closely with the actual risk exposure of the combined positions within the portfolio.

Therefore, the portfolio margining system offsets risks across different instruments with similar underlying assets. It improves capital efficiency compared to traditional margining, which sums up individual margin requirements. However, it introduces more complexity in margin calculation.

Margin calculation methodology

Risk factors

The margin requirement is calculated based on five primary risk factors:

1. Non-delta Market Risk – Measures the worst-case scenario P&L under price and volatility stress tests following the SPAN methodology.
2. Absolute Options Delta – Accounts for liquidation and market impact risk.
3. Net Portfolio Delta – Captures potential delta-hedging costs during liquidation.
4. Futures Positions Margin – Ensures consistency with multi-collateral futures margining.
5. Cross-Asset Netting – Allows margin reductions based on asset correlations.

1. Non-Delta Market Risk (Worst-case scenario loss under stress testing)

This component calculates the worst-case portfolio P&L under multiple price and volatility shock scenarios. The methodology follows the SPAN (Standard Portfolio Analysis of Risk) model but with enhancements to handle options (an important difference is that we consider only the delta-hedged portfolio):

• 23 different market scenarios simulate price movements as an example between -15% to +15%, with additional extreme shocks at -45% and +45%.
• Volatility adjustments based on an option’s historical IV behavior, and forward-looking risk estimates.
• Theta Decay Impact: Additional risk multipliers applied for options with negative theta i.e. those that lose value over time, by shocking the time to expiration and bringing it forward in time.
• Delta-Hedged Stress Testing: By assuming a delta-hedge at the current prices for the price shocks, only the residual risk (high order greeks) is considered.

2. Absolute Options Delta (Market impact of large delta exposures)

Absolute delta measures the total directional exposure of a portfolio. This ensures large positions are margined adequately to reflect liquidation/market impact risk. Although a portfolio can have minimal market risk according to the Non-Delta Market Risk, a high delta portfolio will have a liquidation risk. Therefore, the delta of the options’ position is calculated:

Where MaintenanceMarginFactor is given here. A factor of 2 is used as a buffer.

Example:

1. Compute absolute notional delta exposure:

   (0.5 x 100 x 50) + (-0.3 x 150 x 40)=4300

2. Suppose the maintenance margin factor (mm_factor) is 0.01:

   AbsOptionsDelta = 4300 x0.01 x2 = 86

3. Net Portfolio Delta (Cost of delta hedging prior to liquidation)

Net delta represents the overall directional bias of the portfolio, considering both options and futures positions. This metric is crucial for determining hedging costs before liquidation.

The methodology:

• Considers both options and futures in the portfolio.
• Calculates net delta exposure, incorporating futures hedging.
• Uses the smallest unhedged exposure to determine risk.
• Converts delta exposure to notional value using the index price.
• Applies a dynamic maintenance margin factor to compute the required margin.

Example:

1. Calculate Options Delta:

   options_delta = (0.5 x 100) + (-0.3 x 200) = 50 - 60 = -10

2. Calculate Futures Delta:

   underlying_delta= -80

3. Determine Net Delta Exposure:

   min_net_portfolio_delta =

   = min(abs(options_delta), abs(options_delta + underlying_delta)) =

   = min(10, abs(-10 + (-80))) = 10

   min_net_portfolio_delta is bounded by abs(options_delta) since we only want to consider futures deltas that are offsetting options deltas.

4. Convert to Notional Exposure:

   min_net_portfolio_delta_notional = 10 x 50 = 500

5. Apply Maintenance Margin Factor (ex. mm_factor = 0.01):

   Net Portfolio Delta = 500 x0.01 = 5

4. Futures Positions Margin

Futures margining follows the multi-collateral margining system to ensure that margin requirements for futures remain consistent for the clients that trade only futures; we use the existing margin system for multi-collateral futures.

Margin requirements for futures are summed with the margin requirements calculated for options.

Note: The multi-collateral margining system is slightly different from the one for single collateral contracts. For single collateral, margin requirements are based on the mark price instead of the average entry price. This approach for multi-collateral contracts was chosen since it was deemed easier for clients to understand, since initial margin is fixed for a given size and average entry price.

5. Cross-asset netting (Risk reduction from correlated assets)

Cross-asset netting is a margin reduction mechanism that allows the portfolio margining system to recognize correlated risk offsets across different instruments. Instead of treating all positions as independent, the system applies a correlation factor to reduce overall margin requirements when assets have historically offsetting risks.

The system interpolates between two values:

1. The worst of the summed losses per scenario across all options.
2. The sum of the worst loss per asset across all scenarios (the stricter).

The system interpolates between these methods to balance risk accuracy and capital efficiency. And this interpolated value will be considered the portfolio non-delta market risk. The parameter itself will be set by the administrator and will be between 0 and 1.

Note: This number expresses only the correlation between BTC and ETH, since these are the underlyings of the options that are listed and it is expected to have for some time. If further options are added the methodology needs to be revisited to handle 3+ distinct underlyings.

Example:

Approach 1: Worst of the summed losses per scenario

The losses for each scenario are the result of the sum of the loss of each asset. It assumes that all losses in each scenario are additive, meaning BTC and ETH losses are fully realized together.

The worst-case total across all scenarios is -3000.

Approach 2: Worst loss per asset across all scenarios

Here, we look at the worst loss for each individual instrument across all scenarios:

• Worst BTC loss across all scenarios: -2500 (Scenario 4)
• Worst ETH loss across all scenarios: -2500 (Scenario 2)

The total margin requirement is -2500 + (-2500) = -5000

However, this does not assume BTC and ETH hit their worst losses in the same scenario.

Portfolio-level margin calculation

After calculating the above risk factors for individual positions, the final margin requirement is determined at the portfolio level by integrating these components in a structured manner:

OptionsMaintenanceMargin = max(CrossAssetNettedMarketRisk, AbsOptionsDelta)+ NetPortfolioDelta

We take the max of the two above so that we are still bound by liquidation risk in the case of a carefully hedged portfolio.

OptionsInitialMargin = OptionsMaintenance x MarginOptionsIMarginFactor

PortfolioMaintenanceMargin = OptionsMaintenanceMargin + FuturesMaintenanceMargin

PortfolioInitialMargin = OptionsInitialMargin + FuturesInitialMargin

The OptionsIMarginFactor is defined by the administrator.

In the case of long-only option portfolios, the options initial and maintenance margin cannot be more than the mark price, since this is the maximum loss.