# Delta hedging: units first

**DL-02 · Dealer Logic · Core**

**Lesson question:** How do option sensitivities become futures contracts?

Original fictional examples; educational writing, not live market data, orders or production approval.

## By the end

- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.

**Prerequisites:** DL-01

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.

## Calculation popup: Calculate the hypothetical hedge

```text
Target futures = −book dollars/point ÷ futures dollars/point
```

Fictional inputs, explicit units and fixed other factors.

1. −2,500/50=−50.

2. −3,000/50=−60.

3. Adjustment=−60−(−50)=−10.

**Result:** Sell ten additional futures.

## Graph: Delta hedging: units first—worked comparison

**Horizontal:** Option Delta (USD/index point)  
**Vertical:** Target futures contracts

Fictional data from the written example. The chart organizes the comparison; its shape is not a forecast.

Complete numerical data are embedded in `scripts/dealer-logic/DL-02.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

A notional-only hedge can miss Beta and basis differences. Delta neutrality is not risklessness.

## Check your understanding

### How many additional contracts are sold when the target changes from −50 to −60?

**Answer:** Ten.

**Why:** New target minus existing position is −10.

### What is the critical failure to avoid?

**Answer:** A notional-only hedge can miss Beta and basis differences. Delta neutrality is not risklessness.

**Why:** Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome. **Critical risk check.**

## Takeaway

Return to the question: How do option sensitivities become futures contracts? State the observed facts, the assumptions and the failure condition separately.

## References and provenance

The cited references support definitions and conventions. The teaching prose, tickets and numerical scenarios are original; they are not attributed as historical market observations.

- [OIC Greeks](https://www.optionseducation.org/advancedconcepts/understanding-options-greeks)

- [Cboe 0DTE positioning study, May 2025](https://www.cboe.com/insights/posts/0-dt-es-decoded-positioning-trends-and-market-impact)