# Dealer Charm

**DL-09 · Dealer Logic · Core**

**Lesson question:** Why can the clock change a neutral book?

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

Charm is Delta's calendar-time drift with other inputs fixed. A book can move away from neutrality without a spot trade because the remaining option life changes.

This course defines Charm as the negative derivative with respect to remaining time. Another source's opposite convention must be converted before comparison.

## Understand the mechanism

If Charm is +200 share-equivalents per calendar day, one-quarter day adds approximately +50 option Delta. The offsetting hedge sells 50. A negative sign reverses the direction.

Daily, annual and trading-day displays are different units. Near expiry a fixed daily approximation can become stale during the same day.

## Walk through the process

Check the dominant expiries and inventory changes. Isolate clock effects from spot and IV effects rather than attributing everything to one dealer-flow label.

A modeled clock drift does not specify a compulsory execution time. Desks have different thresholds, objectives and transaction costs.

## 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 hypothetical book begins locally neutral with +200 shares/day of Charm. Six hours are 0.25 calendar day. The option exposure increases about 50 shares, so the new hedge adjustment is −50.

If spot or IV moves during the interval, full revaluation or additional sensitivity terms are needed. The graph shows only the isolated clock contribution.

## Calculation popup: Calculate the hypothetical hedge

```text
dH ≈ −Charm_per_day × elapsed_days
```

Fictional inputs, explicit units and fixed other factors.

1. Six hours=0.25 calendar day.

2. −200×0.25=−50.

**Result:** Sell 50 shares.

## Graph: Dealer Charm—worked comparison

**Horizontal:** Elapsed calendar days  
**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-09.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

Reversing calendar time and remaining time reverses the conclusion. Assuming every expiry creates the same daily flow ignores signed inventory.

## Check your understanding

### What hedge change follows over six hours at +200 shares/calendar day?

**Answer:** Sell about 50 shares.

**Why:** 200×0.25=50 added Delta; hedge oppositely.

### What is the critical failure to avoid?

**Answer:** Reversing calendar time and remaining time reverses the conclusion. Assuming every expiry creates the same daily flow ignores signed inventory.

**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: Why can the clock change a neutral book? 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)