How many additional contracts are sold when the target changes from −50 to −60?
Reveal the worked answer
Ten.
New target minus existing position is −10.
Dealer Logic · DL-02 · Core
Delta hedging: units first
How do option sensitivities become futures contracts?
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: Why dealers hedge
A hedge calculation is a unit conversion before it is a directional narrative. Per-unit Delta, per-contract Delta, share-equivalents and dollars per index point are different quantities. Write the unit next to every number.
Understand the mechanism
Ten standard 100-unit calls at Delta 0.60 contribute +600 share-equivalents. An index book can instead be expressed in dollars of P/L per index point. Dividing that latter sensitivity by a futures contract's dollars per point produces a contract hedge.
Do not divide share-equivalents by futures notional without converting the exposure. A proxy hedge may also need Beta or basis adjustments.
Walk through the process
Net every signed option leg, identify the matching hedge instrument, and use the actual multiplier. Record the observation time because Delta changes.
Calculate target minus existing hedge to estimate an adjustment. A locally neutral result still retains Gamma, Vega, jump, basis and execution risks.
Evidence boundary
The arithmetic is original conditional teaching material, not a measurement of current dealer positions. The cited Cboe research is historical product-specific evidence, not a live inventory feed. Model outputs should remain distinguishable from observed market facts.
A worked example
A fictional index-option book has +2,500 dollars per point of Delta. The teaching future provides 50 dollars per point. Its target hedge is −50 contracts.
If sensitivity rises to +3,000, the target becomes −60. A desk already short fifty would sell ten additional contracts. Selling sixty additional contracts would overhedge. The graph relates book sensitivity to target quantity.
Open the calculation without leaving this lesson
Delta hedging: units first—worked comparison
Vertical: Target futures contracts
Horizontal: Option Delta (USD/index point)
1. Fictional example
Read the graph as a data table
| Option Delta (USD/index point) | Fictional example |
|---|---|
| 2,500 | -50 |
| 3,000 | -60 |
What would invalidate the reading?
A notional-only hedge can miss Beta and basis differences. Delta neutrality is not risklessness.
Check your understanding
Try the question before revealing its answer. These are reading checks, not trading certification or a site completion record.
What is the critical failure to avoid?
Reveal the worked answer
A notional-only hedge can miss Beta and basis differences. Delta neutrality is not risklessness.
Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome.
Return to the question: How do option sensitivities become futures contracts? State the observed facts, the assumptions and the failure condition separately.
Sources, assumptions and downloadable script
External references support definitions and conventions. Worked scenarios and prose are original. No current quotes or dealer inventory are claimed.
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