Volga Calculator
The formula
What the volga (vomma) tells you
The gamma of volatility: how vega grows or shrinks as vol itself moves. Long options carry positive volga — rising vol makes the same vega bet accelerate — which is exactly why tail hedges pay more than vega estimates suggest.
Calculation: Volga (vomma) = ∂ν/∂σ — curvature of value in volatility. Enter your inputs and every substitution is shown below the result.
Reading the result
Volga matters most when big vol moves are the thesis: crisis hedges, pre-event longs, and any straddle you plan to hold through a regime change. In calm regimes volga rounds to zero.
Rules of thumb: Volga is to vega what gamma is to delta: same √T profile, ATM-peaked; meaningful when σ moves ≥5 pts
Limitations and best practice
Do not add volga to vega casually — the curvature is over a full vol-point scale and mixing conventions (per 1% vs per 100%) is the classic desk error. Also smile dynamics dominate single-instrument volga in real crises.
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
Is volga the same as vanna?
Why are straddle traders obsessed with it?
When can volga hurt?
Does volga show in broker risk screens?
Source & methodology
Second-order vol Greeks; standard desk practice.
Volga: the number, the method and the caveats
You are here because you need a specific number, and you want to see how it was produced before you rely on it. There are plenty of pages about Volga; almost none of them show the working. This one does: the formula, every input, a fully computed example, and a sensitivity analysis calculated live from this engine’s own defaults.
The number itself is the easy part. What takes judgement is knowing which inputs are facts in your situation and which are guesses wearing a decimal point — a distinction this page makes explicit for every field above.
In plain terms, Volga answers the question "Volga per 1%² vol (×10,000)?". The measurement matters because it converts a situation that feels complicated — several inputs pulling in different directions — into a single number you can act on. Within Investing & Markets, Options & Derivatives is the context where this figure is quoted most often, and professionals treat it as a first-pass screen rather than a verdict.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to volga per 1%² vol (×10,000) = 0.239 on the default inputs, and the sensitivity section ranks the inputs that move the result — Underlying price first, at ≈704.0 % 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.
Inside the Volga calculation: formula and every input
Here is the complete model this tool runs — Volga (vomma) = ∂ν/∂σ — curvature of value in volatility — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Underlying price ($) (example value 235) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
Strike ($) (example value 111) is a measured number in the unit named by the label; the formula does not convert for you. 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 measured number in the unit named by the label; the formula does not convert for you. Be precise about the boundary (exact date, start of month); time inputs decide the exponent in most formulas.
Risk-free rate (%) (example value 5) is a measured number in the unit named by the label; the formula does not convert for you. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
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. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Option type (example value Call) is a selector, not a measurement: the engine follows a different route for each option. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
A fully worked Volga example
The tool prints its own working; this is the same arithmetic on the example values, reproduced so you can follow it by hand. Starting figures: Underlying price ($), Strike ($), Time to expiry (years), Risk-free rate (%). The computed volga per 1%² vol (×10,000) comes out at 0.239, which the interpretation band labels “Vega itself flexes 0.239 per vol point (×10,000) — an 10-pt vol rise re-prices this option ~$0.00 vs the naive $0.00”.
- Volga = Sφ(d1)√T·d1·d2/(σ·10⁴) = 0.000024 per pt² (×10,000 = 0.239)
- Positive volga: vol up makes you faster at collecting vega (convex) — long options enjoy it
- 10-pt move with curvature: $0.00 vs flat vega estimate $0.00
Naive vega-only 10-pt P&L — $0.00 /share. Read next to the headline, this is the figure that shows the shape of the trade-off.
With volga convexity — $0.00 /share. This is the number experienced users quote when the headline alone would mislead.
Volga bonus/penalty — $0.00 /share. Compare it against the main result of 0.239 before drawing conclusions.
Volga ×10,000 per contract — 23.9. This is the number experienced users quote when the headline alone would mislead.
Keep this worked example open while you enter your own figures: matching the shape of the substitution is the fastest way to spot a unit or convention mistake.
How far Volga can reasonably move
The honest version of any estimate is a corridor, and this one is cheap to produce: Volga was recomputed at 5 points along the dominant input, with every other field left untouched.
| Underlying price setting | Volga per 1%² vol (×10,000) |
|---|---|
| 80 % of the example value | 12.220 |
| 90 % of the example value | 1.923 |
| example inputs | 0.239 |
| 110 % of the example value | 0.026 |
| 120 % of the example value | 0.003 |
Across 5 settings of Underlying price, the result spans 0.003 to 12.220. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Underlying price alone; the substitution steps will follow your figures exactly.
What actually moves your Volga
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 volga per 1%² vol (×10,000) was recalculated from scratch. Read it as a map of where Volga is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Nudge Underlying price by ±10 % and Volga lands between 0.026 and 1.923 (sensitivity ≈704.0 %)
- Strike: ten percent up gives 1.764, ten percent down gives 0.018 — ≈637.5 % of the volga per 1%² vol (×10,000) either way
- Nudge Implied volatility by ±10 % and Volga lands between 0.035 and 0.945 (sensitivity ≈295.2 %)
- Time to expiry: ten percent up gives 0.519, ten percent down gives 0.092 — ≈116.9 % of the volga per 1%² vol (×10,000) either way
- Risk-free rate: ten percent up gives 0.227, ten percent down gives 0.252 — ≈5.4 % of the volga per 1%² vol (×10,000) either way
Underlying price is the dominant lever here: ten percent either way moves the result by about 704.0 %, from 0.026 to 1.923. That is where a careless figure does the most damage, so check it against a source, and treat Strike as the second priority (≈637.5 % 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.
Reading the result: bands, zones and thresholds
A number on its own is trivia; a number against a range is intelligence. The verdict attached to the default calculation — “Vega itself flexes 0.239 per vol point (×10,000) — an 10-pt vol rise re-prices this option ~$0.00 vs the naive $0.00” — is one band on a ladder your own figure may sit somewhere else on. The sensitivity list shows how far a modest input error moves you along that ladder: for Underlying price, ±10 % covers 0.026 to 1.923. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
Placing this figure in context: calculators of this kind differ less in arithmetic than in what they choose to ignore. This one keeps Underlying price ($) explicit so that the omissions are visible rather than hidden in a preset.
How people get Volga wrong
Do not add volga to vega casually — the curvature is over a full vol-point scale and mixing conventions (per 1% vs per 100%) is the classic desk error. Also smile dynamics dominate single-instrument volga in real crises. 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 Naive vega-only 10-pt P&L. The companions are where the shape of the trade-off survives the rounding.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Underlying price dominating — a careful figure there beats false precision everywhere else.
Another is comparing across contexts: a Volga computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
A quick check for any Volga figure
- 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.
- Put Underlying price under a magnifier; the sensitivity table above is the reason why.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Compare the result with one independent method or published benchmark.
- Confirm the answer against one independent method or published benchmark for Volga.
How to use the Volga tool properly
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — start from evidence. The inputs behind Volga 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. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. If a result feels obviously right, that is the moment to check the inputs hardest.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. Estimates improve most when the worst case is written down in ink.
Step 4 — run the scenario trio. Expected, pessimistic, optimistic. The gap between pessimistic and expected is the number to plan against; the optimistic result is useful only as a ceiling. Repeating a calculation with the same numbers proves only that the arithmetic is reliable — which is worth knowing.
Step 5 — save the story with the figure. A number without its inputs and its date is unusable within a quarter. Record 0.239, the assumptions behind it, and today’s date; your future self will be auditing a stranger’s arithmetic. Compare the calculation to the rough guess you arrived with, and ask why they differ.
From calculation to decision: where Volga earns its keep
Most Options & Derivatives disagreements are arithmetic disagreements in disguise. When Volga per 1%² vol (×10,000) of 0.239 sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. The test of a good estimate is not that it feels right but that it changes what you do.
Professionals in Options & Derivatives use this style of calculation as a screening filter before spending real money or effort: a quick Volga check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Treat Volga like a smoke alarm rather than a painting — its value is in being tested periodically, not in being admired once. Half of a good calculation is knowing which input you would hate to be wrong about.
People also ask about Volga
What affects Volga the most?
The short answer: Underlying price. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the volga per 1%² vol (×10,000) recalculated — Underlying price moved it furthest, by roughly 704.0 % (0.026 to 1.923).
Which matters more: strike or underlying price?
By the numbers, Underlying price: a ten-percent change in it moves the result ≈704.0 %, versus ≈637.5 % for Strike. Spend your measuring effort in that order — precision on the weaker lever buys almost nothing.
What is a typical Volga?
With the example inputs on this page the result is 0.239, labelled “Vega itself flexes 0.239 per vol point (×10,000) — an 10-pt vol rise re-prices this option ~$0.00 vs the naive $0.00”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Volga by hand?
Three steps: write the formula (Volga (vomma) = ∂ν/∂σ — curvature of value in volatility), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Volga than any number of calculator runs.
What happens to Volga if underlying price changes by 10 %?
On these inputs a ±10 % change in underlying price takes Volga to 0.026 against the 0.239 example — around 704.0 % of the headline. The same test on every other field is in the sensitivity section.
Is the Volga result of 0.239 good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Volga sit against the 0.239 reference above, how far would a plausible input error move it (≈704.0 % per ten percent on Underlying price), and what does the alternative option compute to?
What is a good Volga?
Markets give away free benchmarks: anything that beats the relevant index after costs earns the label "good", and this tool’s verdict band translates Volga against experience ranges. Before that, check that the inputs are realistic — a great Volga built on optimistic inputs is just a nicer-looking error.
How do I calculate Volga manually?
Write down the inputs, then follow the printed steps in order — Volga (vomma) = ∂ν/∂σ — curvature of value in volatility. A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
Is volga the same as vanna?
Different axis: volga is ∂vega/∂vol (own convexity); vanna is ∂delta/∂vol (cross with spot).
Why are straddle traders obsessed with it?
Because a straddle’s vega grows as vol rises — the long-volga effect that turns a vol bet into a convex one.
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.
Glossary for Volga
- Naive vega-only 10-pt P&L
- $0.00 /share in the default Volga calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- With volga convexity
- $0.00 /share in the default Volga calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Volga bonus/penalty
- $0.00 /share on the example inputs — a companion figure printed beside the headline of Volga so that no result is read in isolation.
- Volga per 1%² vol (×10,000)
- The primary output of this tool: 0.239 for the default inputs, computed exactly from Volga (vomma) = ∂ν/∂σ — curvature of value in volatility.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Vega itself flexes 0.239 per vol point (×10,000) — an 10-pt vol rise re-prices this option ~$0.00 vs the naive $0.00”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Volga 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 Volga model comes from
There is no black box on this page — the engine evaluates Volga (vomma) = ∂ν/∂σ — curvature of value in volatility. Source of record: Second-order vol Greeks; standard desk practice. Where a professional version of this calculation differs, it differs in inputs and jurisdiction-specific coefficients, not in the algebra — which is why re-checking your inputs beats hunting for a second calculator.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. Nothing is smoothed, weighted or adjusted behind the scenes; where judgement enters, this page says so and names the input responsible.
What to do with your Volga next
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.