Vega Calculator
The formula
What the vega tells you
Sensitivity to implied volatility — the bet that the market will pay more (or less) for uncertainty itself, independent of the stock. Most “the stock moved but my option fell” stories are vega stories.
Calculation: ν = Sφ(d1)√T per 100 vol pts → per 1 vol point (closed form). Enter your inputs and every substitution is shown below the result.
Reading the result
Long vega profits when fear re-rates up (crises, events); short vega harvests when fear oozes out (post-event crush). Weigh vega against the vol regime: 5 points of IV on an index is rare; on a meme name it is Tuesday.
Rules of thumb: Index straddle vega ≈ 0.4·S·√T/100; post-event IV crush of 30–50% of the pre-event premium is normal
Limitations and best practice
Vega assumes a parallel shift of the smile, which never happens — skew moves strike-selectively, so your 25-delta put and your ATM call can lose vega money at the same time. And vega decays slowly but surely near expiry.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Why did my call lose money on a rally?
Is vega the same for calls and puts?
How do I hedge vega?
Does vega fall to zero at expiry?
Source & methodology
Hull — BS vega via re-pricing.
Vega: what this tool answers
You are here because you need a specific number, and you want to see how it was produced before you rely on it. Vega is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Vega per 1% vol in real time, and see every substitution printed below.
Return and risk arrive as a package in Vega. A result of $0.16 /share means little until you ask what variance sits behind it, how it compares with the boring alternative (the companion tools above compute exactly that comparison), and whether the inputs assume the good scenario or the expected one.
The useful way to hold Vega is as a ratio with a story attached: ν = Sφ(d1)√T per 100 vol pts → per 1 vol point (closed form) says how the parts combine, and the $0.16 /share figure above is simply that sentence written in numbers. Everything that follows unpacks one clause of the sentence at a time.
Nothing below is stock text pasted around a number: the worked example computes vega per 1% vol = $0.16 /share from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Underlying price first, at ≈56.3 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
How Vega is computed, line by line
The engine implements a single stated model: ν = Sφ(d1)√T per 100 vol pts → per 1 vol point (closed form). There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Underlying price ($) (example value 86) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
Strike ($) (example value 105) is a plain measured quantity — the unit shown in the label is the unit the formula expects. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
Time to expiry (years) (example value 1) is a quantity rather than a category — precision here is cheap and worth having. Use the value as of today, not as of the last time you looked — time fields drift silently.
Risk-free rate (%) (example value 5) is a quantity rather than a category — precision here is cheap and worth having. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Implied volatility (%) (example value 25) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Option type (example value Call) is a choice rather than a quantity — pick the option that matches your situation, because the calculation path branches here. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
The default Vega calculation, written out in full
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Underlying price ($), Strike ($), Time to expiry (years), Risk-free rate (%). Run to the end, the vega per 1% vol resolves to $0.16 /share — One implied-vol point moves the premium $0.16 ($15.98/contract); a 5-point vol crush costs $79.92 per contract before the stock does anything on the bands this tool uses.
- ν = S·φ(d1)·√T ÷ 100 → ν = $0.16
- Vega is largest ATM and grows with √T — long-dated options are vol instruments
- A 4-pt IV crush (post-earnings) on this option = $0.64/share
Vega per contract — $15.98. Read next to the headline, this is the figure that shows the shape of the trade-off.
5-pt vol scenario — $0.80 /contract × 100. This is the number experienced users quote when the headline alone would mislead.
Vega as % of premium — 11.6 per vol-pt. If your inputs change, this is usually the first companion figure to move.
Breakeven vol move — 0.1 vol pts. Read next to the headline, this is the figure that shows the shape of the trade-off.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
Scenario table: Vega at ±10 % and ±20 % of the key input
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Underlying price setting | Vega per 1% vol |
|---|---|
| 80 % of the example value | $0.02 /share |
| 90 % of the example value | $0.07 /share |
| example inputs | $0.16 /share |
| 110 % of the example value | $0.25 /share |
| 120 % of the example value | $0.29 /share |
That spread — $0.02 /share at the low end, $0.29 /share at the high — is what a careful read of Vega looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Underlying price alone; the substitution steps will follow your figures exactly.
What actually moves your Vega
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the vega per 1% vol was recalculated from scratch. For Vega the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Underlying price +10 % → Vega = $0.25 /share · −10 % → $0.07 /share (the vega per 1% vol shifts ≈56.3 %)
- Strike: ten percent up gives $0.08 /share, ten percent down gives $0.23 /share — ≈47.2 % of the vega per 1% vol either way
- Time to expiry: ten percent up gives $0.18 /share, ten percent down gives $0.14 /share — ≈11.4 % of the vega per 1% vol either way
- Implied volatility: ten percent up gives $0.17 /share, ten percent down gives $0.14 /share — ≈11.0 % of the vega per 1% vol either way
- Nudge Risk-free rate by ±10 % and Vega lands between $0.16 /share and $0.16 /share (sensitivity ≈1.2 %)
Underlying price is the dominant lever here: ten percent either way moves the result by about 56.3 %, from $0.07 /share to $0.25 /share. Spend your verification effort there first, and treat Strike as the second priority (≈47.2 % per ten percent). The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
What a Vega of $0.16 /share means in practice
The value above only becomes useful the moment you know what it is being measured against. The default case lands in the “One implied-vol point moves the premium $0.16 ($15.98/contract); a 5-point vol crush costs $79.92 per contract before the stock does anything” band, and bands are deliberately wide because real situations overlap. How much of that band is luck? On Underlying price alone ten percent either way covers $0.07 /share to $0.25 /share. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
Set Vega beside its neighbours and it usually plays a specific role: this figure establishes the size of something, and the neighbouring tools establish whether that size is acceptable. Skipping the first step makes the second one arbitrary.
The errors that quietly break a Vega figure
Vega assumes a parallel shift of the smile, which never happens — skew moves strike-selectively, so your 25-delta put and your ATM call can lose vega money at the same time. And vega decays slowly but surely near expiry. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Reporting the headline and quietly discarding Vega per contract. The companions are where the shape of the trade-off survives the rounding.
This model has its own particular trap: Underlying price carries ≈56.3 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
A final trap is presentation: reporting Vega to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Vega verification checklist
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Verify each input against its original source document, not memory.
- Check Underlying price before anything else: it is the measured dominant input, ≈56.3 % of Vega per ten percent.
- Confirm the example values are plausible for your own situation before replacing them.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
Step by step: getting a trustworthy Vega out of this tool
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Vega takes a minute to learn and applies to every input above.
Step 1 — start from evidence. The inputs behind Vega are underlying price ($), strike ($), time to expiry (years), risk-free rate (%), implied volatility (%), option type. Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. The input you reach for first is usually the one you measured longest ago.
Step 2 — enter the conservative case first. Resist the flattering scenario. Type the inputs you would defend in front of a sceptical reader, read the Vega per 1% vol ($0.16 /share for the example values), and note the verdict band. Most surprises in numbers are surprises about inputs, not about formulas.
Step 3 — change one input at a time. Nudge a single field by ten percent, watch the headline and its companions move, then undo it. Two or three fields will dominate — the sensitivity table above already ranks them for this engine. A result worth acting on survives having its two shakiest inputs halved.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Vega from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. A figure with a date beside it becomes evidence; without one it stays an anecdote.
Step 5 — write the one-line memo. “Vega per 1% vol = $0.16 /share on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. Half of a good calculation is knowing which input you would hate to be wrong about.
Who actually uses Vega — and when
In Options & Derivatives the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. The test of a good estimate is not that it feels right but that it changes what you do.
The audience for this page is people who need one trustworthy number before their next decision. In professional Options & Derivatives practice the pattern is always the same — screen with Vega, then invest slow analysis only in whatever survives the screen. The point of transparency is that a reader can disagree with a specific line rather than with you.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Investing & Markets the expensive mistakes are rarely sudden; they are small changes in Underlying price ($) that nobody recalculated for a year. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
People also ask about Vega
What affects Vega the most?
Measured on this engine, Underlying price is the dominant lever: moving it ±10 % shifts the vega per 1% vol across $0.07 /share to $0.25 /share — about 56.3 % of the headline, with Strike next at ≈47.2 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: strike or underlying price?
For Vega, Underlying price wins the head-to-head (≈56.3 % against ≈47.2 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Vega?
There is no honest universal average for Vega, but there is a reference point: the defaults on this page produce $0.16 /share (One implied-vol point moves the premium $0.16 ($15.98/contract); a 5-point vol crush costs $79.92 per contract before the stock does anything). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Vega by hand?
Use the stated model — ν = Sφ(d1)√T per 100 vol pts → per 1 vol point (closed form) — and substitute in the order the tool prints (it starts from ν = S·φ(d1)·√T ÷ 100 → ν = $0.16). On the example inputs the hand route lands on $0.16 /share, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Vega if underlying price changes by 10 %?
On these inputs a ±10 % change in underlying price takes Vega to $0.25 /share against the $0.16 /share example — around 56.3 % of the headline. The same test on every other field is in the sensitivity section.
Is the Vega result of $0.16 /share good or bad?
Neither, on its own — the label “One implied-vol point moves the premium $0.16 ($15.98/contract); a 5-point vol crush costs $79.92 per contract before the stock does anything” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Underlying price alone moves it by ≈56.3 %.
Can I predict future returns with Vega?
No tool predicts; Vega computes implications. Use it to ask "if these inputs hold, what follows" — then stress the assumptions.
Does Vega account for fees and taxes?
Only what you put in. Fees belong inside Underlying price ($) where they shrink returns before compounding touches them; taxes are outside the scope of a pre-tax Vega and should be layered on top before decisions.
Why did my call lose money on a rally?
Likely a vol crush (earnings over, fear gone) larger than the delta gain — that is classic long-vega risk unwinding.
Is vega the same for calls and puts?
At the same strike and expiry, parity forces them to be equal — vol hits both sides of the line.
Is my data private on this page?
Yes — computation happens locally in your browser, with no account, no tracking of your inputs and nothing sent to a server. The printed formula is the whole story of what happens to your figures.
What the labels on this page mean
- Vega per contract
- $15.98 for the Vega worked case; it sits next to the main result because it carries context the headline leaves out.
- 5-pt vol scenario
- $0.80 /contract × 100 for the Vega worked case; it sits next to the main result because it carries context the headline leaves out.
- Vega as % of premium
- 11.6 per vol-pt on the example inputs — a companion figure printed beside the headline of Vega so that no result is read in isolation.
- Vega per 1% vol
- The primary output of this tool: $0.16 /share for the default inputs, computed exactly from ν = Sφ(d1)√T per 100 vol pts → per 1 vol point (closed form).
- Worked example
- Every substitution in order, from the example inputs to $0.16 /share — the audit trail for the headline figure.
- Verdict band
- The plain-language label — here “One implied-vol point moves the premium $0.16 ($15.98/contract); a 5-point vol crush costs $79.92 per contract before the stock does anything” — mapping the computed figure onto experience-based ranges for Investing & Markets.
- Sensitivity (±10 %)
- How far the Vega moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Where the Vega model comes from
Everything above runs on one stated formula, applied without hidden coefficients: ν = Sφ(d1)√T per 100 vol pts → per 1 vol point (closed form). Source of record: Hull — BS vega via re-pricing. Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
Turning this Vega into a decision
Save the number together with its inputs and today’s date; a Vega figure without context is unusable the moment an input changes.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Investing & Markets, a dated figure is a trend, and an undated one is a rumour.