Can ATM Gamma rise as IV falls?
Reveal the worked answer
Yes under the stated vanilla-model comparison.
Different sensitivities must be calculated separately.
Dealer Logic · DL-10 · Core
Volatility changes specific sensitivities
Which Greek changes when IV falls?
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
'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.
Volatility changes specific sensitivities—worked comparison
Vertical: Gamma per USD
Horizontal: IV (%)
1. Fictional example
Read the graph as a data table
| IV (%) | Fictional example |
|---|---|
| 10 | 0.13914 |
| 15 | 0.0927479 |
| 20 | 0.0695484 |
| 25 | 0.0556259 |
| 30 | 0.0463418 |
| 35 | 0.0397083 |
| 40 | 0.0347314 |
| 45 | 0.0308589 |
| 50 | 0.0277594 |
| 55 | 0.0252222 |
| 60 | 0.0231067 |
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
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 low-premium, low-IV option can still have substantial near-strike Gamma. Using premium size as a complete measure of sensitivity misses that concentration.
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: Which Greek changes when IV falls? 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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