Plain English
Vega is your exposure to the market’s volatility assumption.
Black–Scholes & Greeks · BSM-10 · Core
Vega
What does Vega measure, in which units, and what does it not predict?
How to read 0.12
A one-volatility-point rise, such as 25% to 26%, adds about $0.12.
Typical sign
Long vanilla calls and puts have positive Vega.
Where it matters
Longer-dated and near-the-money options often carry more Vega.
What you will learn and prerequisites
- Explain Vega in plain language.
- Reproduce the unit conversion.
- Compare a local estimate with model revaluation.
Read first: Read the notation
Vega measures sensitivity to the volatility input. Moving from 25% to 26% is one volatility point, or 0.01 in decimal sigma. It is not the same as increasing 25% by one percent relative, which gives 25.25%.
Vega is market terminology, not the name of a Greek letter.
Read the derivative as a sentence
Raw Vega differentiates with respect to 1.00 decimal volatility. Dividing by 100 produces the per-point display. Matching standard European calls and puts have equal positive Vega.
Implied volatility is inferred from an option price under a model. It does not guarantee future realized movement. A sensitivity number says nothing by itself about whether volatility is cheap.
Use it within its scope
A one-point shock is a useful local experiment. Larger shocks change Vega through Vomma and can interact with spot. Full repricing is preferable to extrapolating one Vega over an enormous move. A directional winner can still lose from an IV decline.
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 Vega is 11.399767588205. The displayed convention gives 0.113997675882 option-value change per volatility point. Isolate IV +1 volatility point while holding every other input fixed.
Starting option value is 2.977574155222. The local estimate after the shock is 3.091571831104; a full-model recomputation gives 3.091571458721. Approximation minus recomputation is +0.000000372384. 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
Vega across controlled states
Vertical: option-value change per volatility point
Horizontal: IV (%)
1. Fictional example
Read the graph as a data table
| IV (%) | Fictional example |
|---|---|
| 10 | 0.113705 |
| 12 | 0.113829 |
| 14 | 0.1139 |
| 16 | 0.113944 |
| 18 | 0.11397 |
| 20 | 0.113986 |
| 22 | 0.113995 |
| 24 | 0.113998 |
| 26 | 0.113997 |
| 28 | 0.113993 |
| 30 | 0.113986 |
| 32 | 0.113977 |
| 34 | 0.113966 |
| 36 | 0.113954 |
| 38 | 0.11394 |
| 40 | 0.113925 |
| 42 | 0.113908 |
| 44 | 0.11389 |
| 46 | 0.113871 |
| 48 | 0.11385 |
| 50 | 0.113829 |
| 52 | 0.113806 |
| 54 | 0.113783 |
| 56 | 0.113758 |
| 58 | 0.113732 |
| 60 | 0.113705 |
A correct number can be misread
The stated unit is option-value 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 Vega in this example?
Reveal the worked answer
0.113997675882 option-value 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 Vega 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
- Keep spot and time fixed; apply +1 IV point.
- Read Vega/vol point and compare its estimated change with repricing.
- Repeat with +10 points to see why constant Vega is only an approximation.
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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