Question it answers
If nothing else changes, how will my volatility sensitivity evolve?
Black–Scholes & Greeks · BSM-20 · Advanced
Veta
What does Veta measure, in which units, and what does it not predict?
Relationship
Vega itself has time decay.
Use
Important when managing volatility exposure through time.
Sign
Depends on the option state.
What you will learn and prerequisites
- Explain Veta in plain language.
- Reproduce the unit conversion.
- Compare a local estimate with model revaluation.
Veta asks how volatility sensitivity changes through time. It changes Vega, not price directly. Adding it to P/L as though it were Theta answers the wrong question.
This lesson displays daily change in Vega already quoted per volatility point.
Read the derivative as a sentence
Two conversions are needed: divide by 365 for a calendar day and by 100 because the affected Vega is point-scaled. A platform displaying daily change in raw Vega would show a different number.
The sign is state-dependent. Near-money Vega commonly declines toward expiry, but that observation is not a universal statement about every strike or book.
Use it within its scope
A long-volatility position can own less Vega later without any new trades. Reassess exposures before an event rather than assuming the original hedge and premium sensitivity persist. Keep the valuation date explicit.
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 Veta is -68.892452960960. The displayed convention gives -0.001887464465 Vega-per-point change per calendar day. Isolate one calendar day passing while holding every other input fixed.
Starting Vega per volatility point is 0.113997675882. The local estimate after the shock is 0.112110211417; a full-model recomputation gives 0.112093899522. Approximation minus recomputation is +0.000016311895. 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
Veta across controlled states
Vertical: Vega-per-point change per calendar day
Horizontal: Calendar days remaining
1. Fictional example
Read the graph as a data table
| Calendar days remaining | Fictional example |
|---|---|
| 1 | -0.0104374 |
| 2 | -0.0073779 |
| 3 | -0.00602205 |
| 5 | -0.00466159 |
| 7 | -0.00393717 |
| 10 | -0.00329082 |
| 15 | -0.00268252 |
| 20 | -0.00231931 |
| 30 | -0.00188746 |
| 45 | -0.00153348 |
| 60 | -0.00132145 |
| 90 | -0.00106825 |
A correct number can be misread
The stated unit is Vega-per-point change per calendar day. 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 Veta in this example?
Reveal the worked answer
-0.001887464465 Vega-per-point change per calendar day.
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 Veta 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/vol point at 30 days and then 29 days.
- Compare the change with Veta/vol point/day.
- Check both the /100 volatility scaling and /365 day scaling.
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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