Question it answers
If vol moves again, will my Vega be larger or smaller?
Black–Scholes & Greeks · BSM-15 · Advanced
Vomma / Volga
What does Vomma / Volga measure, in which units, and what does it not predict?
Relationship
Vega is the first derivative; Vomma is the next layer.
Sign
Depends on moneyness and the market state.
Use
Important for larger volatility shocks.
What you will learn and prerequisites
- Explain Vomma / Volga in plain language.
- Reproduce the unit conversion.
- Compare a local estimate with model revaluation.
Vomma measures how Vega changes as volatility changes. It is also called Volga. It adds the curvature missing from a constant-Vega estimate.
A long option need not have positive Vomma everywhere. Its sign in this model depends on d1×d2.
Read the derivative as a sentence
Two volatility-point conversions produce the /10,000 display: the affected Vega is already per point, and the new IV move is also measured in points. Raw Vomma times 0.01 instead estimates change in raw Vega.
For price P/L, the quadratic term is one-half Vomma_raw×dSigma². Keep the half and unit conversions separate.
Use it within its scope
Compare small and larger shocks rather than assigning permanent convexity from a strategy name. Near some ATM states the derivative is negative. Paying for long volatility still requires a view on realized movement, IV repricing and costs.
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 Vomma / Volga is -0.004591139275. The displayed convention gives -0.000000459114 Vega-per-point change per volatility point. Isolate IV +1 volatility point while holding every other input fixed.
Starting Vega per volatility point is 0.113997675882. The local estimate after the shock is 0.113997216768; a full-model recomputation gives 0.113996792281. Approximation minus recomputation is +0.000000424487. 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
Vomma / Volga across controlled states
Vertical: Vega-per-point change per volatility point
Horizontal: IV (%)
1. Fictional example
Read the graph as a data table
| IV (%) | Fictional example |
|---|---|
| 10 | 8.17744e-05 |
| 12 | 4.59213e-05 |
| 14 | 2.74286e-05 |
| 16 | 1.68318e-05 |
| 18 | 1.02406e-05 |
| 20 | 5.85545e-06 |
| 22 | 2.76612e-06 |
| 24 | 4.78244e-07 |
| 26 | -1.29242e-06 |
| 28 | -2.71722e-06 |
| 30 | -3.90363e-06 |
| 32 | -4.9214e-06 |
| 34 | -5.81712e-06 |
| 36 | -6.62275e-06 |
| 38 | -7.36067e-06 |
| 40 | -8.0469e-06 |
| 42 | -8.6931e-06 |
| 44 | -9.30789e-06 |
| 46 | -9.89773e-06 |
| 48 | -1.04675e-05 |
| 50 | -1.10211e-05 |
| 52 | -1.15614e-05 |
| 54 | -1.20907e-05 |
| 56 | -1.26108e-05 |
| 58 | -1.31232e-05 |
| 60 | -1.36291e-05 |
A correct number can be misread
The stated unit is Vega-per-point 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 Vomma / Volga in this example?
Reveal the worked answer
-0.000000459114 Vega-per-point 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 Vomma / Volga 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 Vega per point; raise IV by one point and compare.
- Read Vomma's unit as the change in Vega-per-point per volatility point.
- Do not confuse that derivative with the ½-weighted curvature contribution to price.
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.
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