# Volatility changes specific sensitivities

**DL-10 · Dealer Logic · Core**

**Lesson question:** Which Greek changes when IV falls?

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

'Lower volatility means lower option sensitivity' is too vague. Price, Delta, Gamma and Vega are different outputs. A lower premium can coexist with a more concentrated hedge ratio near the strike.

Name the Greek and moneyness before describing the risk change.

## Understand the mechanism

In the smooth BSM model near the money, lower sigma can sharpen Delta's transition and increase Gamma. Away from the strike the behavior can differ. A signed multi-leg book adds further offsets.

Vega and Vanna have separate state dependence. An event-volatility decline may reduce value while raising a particular curvature exposure.

## Walk through the process

Compare controlled states with only IV changed. Record every relevant Greek and the fixed spot, strike and maturity. For actual portfolios, repeat across the surface instead of applying one blanket phrase.

Observed price behavior does not establish inventory sign; mathematical sensitivity and dealer allocation remain separate questions.

## 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

The fictional graph uses S=K=100, 30 days remaining, zero rate and yield. Gamma is computed as phi(d1)/(S×sigma×sqrt(T)) while IV varies from 10% to 60%.

The near-ATM curve shows Gamma rising as IV falls under these assumptions. It is not a rule for every strike or a prediction of future realized volatility.

## Graph: Volatility changes specific sensitivities—worked comparison

**Horizontal:** IV (%)  
**Vertical:** Gamma per USD

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-10.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

A low-premium, low-IV option can still have substantial near-strike Gamma. Using premium size as a complete measure of sensitivity misses that concentration.

## Check your understanding

### Can ATM Gamma rise as IV falls?

**Answer:** Yes under the stated vanilla-model comparison.

**Why:** Different sensitivities must be calculated separately.

### What is the critical failure to avoid?

**Answer:** A low-premium, low-IV option can still have substantial near-strike Gamma. Using premium size as a complete measure of sensitivity misses that concentration.

**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: Which Greek changes when IV falls? 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 Gamma](https://www.optionseducation.org/advancedconcepts/gamma)

- [OIC Vega](https://www.optionseducation.org/advancedconcepts/vega)