Option Stress Testing: Joint Scenarios, Repricing, and Funding

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

An option stress test fully reprices the whole account under deliberately adverse, internally consistent assumptions. It should combine underlying gaps, changes in volatility level and skew, elapsed time, correlation or basis breaks, executable bid-ask costs, and the cash effects of margin, exercise, assignment, and settlement. The result is a conditional vulnerability estimate, not a forecast, probability, worst-case guarantee, or standardized pass/fail score.

Keep two outputs separate. Economic stress loss estimates the decline in executable account value. Funding stress asks whether cash and committed borrowing can meet margin calls, delivery payments, and settlement obligations on time. A portfolio can survive the first test and still fail the second.

Build and run the test

Freeze a timestamp and inventory every option leg, underlying position, cash balance, open order, fee, dividend, borrow obligation, and settlement deliverable. Document how current and scenario liquidation values use bids, offers, sizes, and multi-leg execution assumptions. Then calculate, for scenario s:

P&L_s = V_s^liq - V_0^liq + CF_s

L_s = max(-P&L_s, 0)

B_s = C_0 + F_0 - M_s - S_s

Here, V^liq is executable liquidation value, CF_s is other scenario cash flow, L_s is stress loss, and B_s is the funding buffer after available cash C_0, committed funding F_0, margin calls M_s, and settlement or delivery cash S_s. Avoid counting the same premium, stock delivery, or margin debit twice.

1. Choose purpose and horizon. Test an overnight gap, a delayed exit, expiration processing, or a multi-day liquidation; the horizon determines time decay, path, and available actions.
2. Construct coherent shocks. Combine historical episodes with hypothetical moves beyond the sample. Shock each expiry and strike region, not only one at-the-money volatility number, and weaken offsets whose correlations or basis may break.
3. Fully reprice every leg. Use contract-specific exercise style, settlement, dividends, rates, borrow, and corporate-action terms. Greeks are local diagnostics; large moves and interacting shocks require nonlinear repricing.
4. Convert model value to executable value. Stress bid-ask width, displayed depth, fill size, legging risk, halts, and the time needed to exit. A theoretical mark is not a promised trade price.
5. Apply precommitted limits. Record maximum L_s, minimum B_s, concentration and executable-size limits, plus the action assigned to each breach. Re-run after fills, rolls, partial closes, large market moves, or changed broker requirements.

A reverse stress test starts with a breached limit and searches for combinations that cause it. It is especially useful for exposing hidden concentration or funding dependence, but it does not assign a probability to the resulting scenario.

Worked example

Assume a $100,000 account holds index and single-stock options. One joint scenario applies an -8% index gap, +15 volatility points to short expiries, +8 points to later expiries, a +6-point downside-skew steepening, 1 day of decay, weaker diversification, and bid-ask spreads that widen by 2 times.

The rows are successive valuations, not losses to add together. The scenario stress loss is $6,000, leaving estimated equity of $94,000. A separate assignment-and-settlement map shows a possible $12,000 delivery payment. That amount is not automatically an additional trading loss, but it can breach the funding limit before the portfolio can be closed.

Risks and limitations

• Scenario omission: the damaging path or combination may be absent, even when every individual shock looks severe.
• Model risk: volatility surfaces, early-exercise logic, dividends, rates, borrow, and corporate actions can be specified incorrectly.
• Execution risk: quoted depth can vanish, spreads can gap wider, and multi-leg orders may fill unevenly.
• Changing offsets: Delta, Gamma, Vega, correlations, and basis relationships change through the scenario.
• Funding timing: margin increases or assignment can consume cash before hedges can be sold or settlement proceeds arrive.
• Governance risk: a test has little value if positions, assumptions, limits, and breach actions are not recorded and refreshed.

Common misconceptions

• “Expiration payoff is enough.” Interim volatility, path, margin, assignment, and liquidity can dominate before expiration.
• “Adding separate Greek shocks captures the portfolio.” Linear and one-factor approximations miss curvature and interactions in large joint moves.
• “Margin is the stress loss.” Margin is a collateral requirement; it can be lower or higher than economic loss and can change under house rules.
• “Passing proves the trade is safe.” It shows only that the selected inventory, scenarios, models, and execution assumptions stayed within selected limits.

Related topics

• Position sizing by stress loss
• Net option Greeks
• Implied volatility
• Assignment risk

Authoritative sources

• Characteristics and Risks of Standardized Options - The Options Clearing Corporation
• FINRA Rule 4210: Margin Requirements - FINRA
• Interagency Supervisory Guidance on Stress Testing - Federal Reserve
• Cboe American- and European-Style Theoretical Options Calculation Methodology - Cboe Global Indices
• Black and Scholes (1973), The Pricing of Options and Corporate Liabilities - Journal of Political Economy