Question it answers
Will a volatility shock increase or reduce my spot convexity?
Black–Scholes & Greeks · BSM-18 · Advanced
Zomma
What does Zomma measure, in which units, and what does it not predict?
Relationship
Gamma is not fixed when implied volatility changes.
Use
Useful in convex books during volatility shocks.
Sign
State-dependent.
What you will learn and prerequisites
- Explain Zomma in plain language.
- Reproduce the unit conversion.
- Compare a local estimate with model revaluation.
Zomma connects spot curvature and volatility. It asks whether Gamma becomes larger or smaller after an IV change. That is a different question from Vega's change in option value.
This distinction prevents the blanket claim that lower IV reduces every type of option sensitivity.
Read the derivative as a sentence
Near the ATM state used here, d1×d2−1 is negative, giving negative Zomma. Higher IV reduces the sharpness of the Delta transition; lower IV can increase it. Other states and signed portfolios differ.
The display is Gamma change per one volatility point. Raw and point-scaled derivatives must not be mixed.
Use it within its scope
Stress spot and IV jointly when managing convexity. Recalculate after a major event rather than retaining the earlier Gamma profile. A small premium does not guarantee a small sensitivity of the hedge ratio.
The model boundary
The smooth formulas require positive spot, strike, volatility and remaining time. Zero time and zero volatility still admit explicit value limits, but smooth Greek availability needs separate rules. No invalid or zero input is silently replaced with a default. Continuous dividends, constant parameters and European exercise are modeling assumptions, not claims about every real option.
One complete numerical experiment
The shared fictional European call uses spot 100, strike 100, 30 calendar days, sigma 25%, continuous rate 4% and yield 1%. Its BSM value is 2.977574155; d1=0.070239317 and d2=-0.001433455. Values are per option unit before contract multiplication.
Raw Zomma is -0.221937819262. The displayed convention gives -0.002219378193 Gamma change per volatility point. Isolate IV +1 volatility point while holding every other input fixed.
Starting Gamma is 0.055478868929. The local estimate after the shock is 0.053259490737; a full-model recomputation gives 0.053344652798. Approximation minus recomputation is -0.000085162062. The difference shows the limitation of a local derivative, not a claim that the market must follow either number.
The graph varies only its labeled horizontal input. It is a series of controlled states, not historical observations or a future trajectory. Read its units before interpreting sign or magnitude.
Open the calculation without leaving this lesson
Zomma across controlled states
Vertical: Gamma change per volatility point
Horizontal: IV (%)
1. Fictional example
Read the graph as a data table
| IV (%) | Fictional example |
|---|---|
| 10 | -0.0137347 |
| 12 | -0.00957092 |
| 14 | -0.00704651 |
| 16 | -0.00540249 |
| 18 | -0.00427283 |
| 20 | -0.00346351 |
| 22 | -0.00286404 |
| 24 | -0.00240769 |
| 26 | -0.00205232 |
| 28 | -0.0017702 |
| 30 | -0.00154251 |
| 32 | -0.00135609 |
| 34 | -0.00120156 |
| 36 | -0.00107202 |
| 38 | -0.000962378 |
| 40 | -0.000868749 |
| 42 | -0.000788164 |
| 44 | -0.000718307 |
| 46 | -0.000657356 |
| 48 | -0.000603859 |
| 50 | -0.000556649 |
| 52 | -0.000514777 |
| 54 | -0.000477468 |
| 56 | -0.000444084 |
| 58 | -0.000414091 |
| 60 | -0.000387046 |
A correct number can be misread
The stated unit is Gamma change per volatility point. Mixing raw decimal derivatives with point shocks or calendar time with remaining time can magnify or reverse the result.
The controlled comparison also omits live spread, surface dynamics, unsupported exercise effects and execution. A local sensitivity is not a market forecast or a guarantee of realized P/L.
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 displayed Zomma in this example?
Reveal the worked answer
-0.002219378193 Gamma change per volatility point.
Always state the unit.
Does model agreement prove the same live-market change?
Reveal the worked answer
No.
Actual inputs, instrument features and executable quotes can differ.
Translate Zomma into its specific input, affected quantity and unit before applying it. Revalue when the local approximation no longer fits.
Try it in the working lab
- Record Gamma at 25% IV and then 26% IV.
- Compare the change with Zomma/vol point.
- Check why falling IV is not a universal reduction in every sensitivity.
Your live inputs are independent of the fixed worked example above. Return to the “Lesson example” preset to reproduce it.
My reading record
Personal review marks are not quiz passes, course certification or trading approval. Old plugin progress is not overwritten.
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.
Read this lesson as Markdown · Download its JavaScript content module