# Dealer Vanna

**DL-08 · Dealer Logic · Core**

**Lesson question:** How can IV change the hedge without a spot move?

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

Vanna links Delta and implied volatility. A volatility change can alter directional exposure even while spot is quiet. Maintaining an old hedge can therefore leave a new residual Delta.

The direction is not determined by 'IV rose' or 'IV fell' alone; signed book Vanna is required.

## Understand the mechanism

For a small parallel IV shift, dDelta≈Vanna×dIV, and the neutralizing hedge takes the opposite sign. A per-volatility-point number uses 25%→26% as +1; raw decimal Vanna uses +0.01.

Real surfaces often move nonparallel across strikes and expiries. One scalar can conceal materially different local changes.

## Walk through the process

Declare the inventory sign, units and surface shock. Calculate the local change separately from Gamma and Charm. Then stress alternative skew and term-structure movements.

Do not generalize a buy-flow story from one assumed book to every volatility decline.

## 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

Book Vanna is hypothetically +500 share-equivalents per vol point. IV falls from 25% to 23%, or −2 points. Option Delta changes by approximately −1,000 shares, so a neutralizing hedge buys 1,000.

If signed Vanna were −500, the same event would imply selling 1,000. The graph fixes the positive-Vanna case and varies the shock.

## Calculation popup: Calculate the hypothetical hedge

```text
dH ≈ −Vanna_per_point × dIV_points
```

Fictional inputs, explicit units and fixed other factors.

1. 25%→23% is −2 points.

2. Option dDelta=500×(−2)=−1,000.

3. Opposite hedge=+1,000.

**Result:** Buy 1,000 shares.

## Graph: Dealer Vanna—worked comparison

**Horizontal:** IV change (vol points)  
**Vertical:** Hedge change (shares)

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-08.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

An unsigned Vanna narrative can predict the wrong direction. Mixing raw and point-scaled units creates a factor-of-100 error.

## Check your understanding

### What hedge change follows from +500 shares/vol point and a −2-point IV move?

**Answer:** Buy 1,000 shares.

**Why:** The hedge offsets the −1,000 option-Delta change.

### What is the critical failure to avoid?

**Answer:** An unsigned Vanna narrative can predict the wrong direction. Mixing raw and point-scaled units creates a factor-of-100 error.

**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 can IV change the hedge without a spot move? 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)