A portfolio can be close to delta neutral and still lose heavily. Delta describes a small local price change; it does not summarize jumps, volatility repricing, time decay, exercise or funding needs. Stress testing asks what happens under explicit alternative market states.
Build a position inventory
Record each underlying, contract, quantity, multiplier, deliverable, expiration and direction. Include stock, futures, working orders and any cash obligations created by assignment. Separate actual cash from amounts already committed as collateral. Greeks must use consistent units before they can be combined.
Delta in shares of stock A cannot simply cancel delta in shares of stock B. Converting to dollar exposure or a common factor requires prices and a relationship assumption. Historical beta is an estimate; it may fail when a company has its own news.
A local approximation
For one underlying, a common short-horizon approximation is ΔV ≈ D·ΔS + ½G·(ΔS)² + V·ΔIV + Θ·Δt. Here D is portfolio dollars per $1 stock move, G dollars per squared $1 move, V dollars per one volatility percentage point, and Θ dollars per calendar day. The Greeks already include signed quantities and multipliers.
With D = 200, G = −20, V = −$150 per point and Θ = +$40 per day, a $5 stock fall, four-point IV rise and one elapsed day give −$1,000 − $250 − $600 + $40 = −$1,810. This is an approximation, not an exact repricing or loss ceiling.
Use a scenario grid
| Scenario | What to change | What to inspect |
|---|---|---|
| Gap down | Stock −10%, downside IV higher | Nonlinear losses and short-put funding |
| Rally | Stock +10%, IV lower | Short calls and capped upside |
| Event passes | Little price change, near-term IV falls | Long premium and calendar exposure |
| Liquidity shock | Wider spreads, reduced size | Cash required to exit, not just model value |
Reprice each contract for large shocks, including different volatility changes by strike and expiry. Close to expiration or a discontinuity, a Taylor approximation can be poor. Preserve internally coherent assumptions: stock and index shocks may differ, and an option’s settlement reference may differ from the hedge instrument.
Include the path to settlement
A profitable final scenario can still trigger a margin shortfall along the way. Test earlier dates, an assigned leg, a missing borrow and an unavailable exit. Report economic P/L, peak funding need and executable liquidation estimate separately. A scenario set reveals vulnerabilities; it does not attach probabilities unless those probabilities are explicitly modeled and justified.
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Reviewed . Examples are illustrative; verify exact contract and broker terms.
References: OIC: volatility and the Greeks; FINRA Rule 4210.