Vanna Calculator
The formula
What the vanna tells you
The cross-derivative of vol and spot: how delta responds when implied volatility moves. Vanna is why vol selling and spot rallies reinforce each other — and why unwind days look like both happening in reverse at once.
Calculation: Vanna = ∂Δ/∂σ = −φ(d1)·d2/σ per vol point (closed form). Enter your inputs and every substitution is shown below the result.
Reading the result
When dealers are short OTM put vanna and vol falls, their short delta shrinks — they must buy stock to stay neutral, lifting spot, compressing vol further: the classic slow-bull vanna squeeze. The output numbers size that flow.
Rules of thumb: SPX 90–95% puts concentrate the market’s vanna; vol-selling episodes historically hedge-mobilize $10–30B+ notional
Limitations and best practice
Vanna flows are conditional and reflexive — they amplify regimes, not predict them. Reading a single option’s vanna without the dealer’s net vanna positioning across the chain is the map that is not the territory.
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
What is a vanna squeeze?
Is vanna the same as volga?
Why do OTM puts dominate vanna?
Do options buyers care?
Source & methodology
Dealer-flow literature; standard mixed derivative.
Vanna: 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. Searchers land on a Vanna page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
Return and risk arrive as a package in Vanna. A result of -0.001 /Δ/vol-pt 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.
Every investing metric in Investing & Markets is a bet about the future priced in today’s language. Vanna translates that bet: Vanna = ∂Δ/∂σ = −φ(d1)·d2/σ per vol point (closed form). The translation is mechanical and reliable; the judgement is deciding whether the inputs you feed it are honest forecasts or wishful numbers.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here vanna per 1% vol = -0.001 /Δ/vol-pt, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Underlying price first, at ≈361.1 % 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.
The Vanna formula, explained
The engine implements a single stated model: Vanna = ∂Δ/∂σ = −φ(d1)·d2/σ per 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 160) is a measured number in the unit named by the label; the formula does not convert for you. If your source quotes a figure before and after some deduction, decide which one the formula wants and be consistent for every field.
Strike ($) (example value 104) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Time to expiry (years) (example value 1) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Use the value as of today, not as of the last time you looked — time fields drift silently.
Risk-free rate (%) (example value 5) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Implied volatility (%) (example value 22) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Option type (example value Call) is a categorical input — the option you choose decides which numbers the formula uses. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Vanna with real numbers, step by step
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Underlying price ($), Strike ($), Time to expiry (years), Risk-free rate (%). The endpoint of that chain is -0.001 /Δ/vol-pt of vanna per 1% vol, sitting in the “Each implied-vol point shifts delta -0.0006 — a 5-pt IV spike re-hedges this position by -0.003 delta before the stock moves at all” band.
- Vanna = −φ(d1)·d2/(σ·100) per vol pt = -0.00058
- OTM puts have the largest positive vanna; this is the engine of “vol-selling squeeze”
- 10 contracts: the 5-pt scenario creates -$462 of forced hedging demand
Δ-shift on 5-pt vol move — -0.003. Read next to the headline, this is the figure that shows the shape of the trade-off.
Δ-shift on 10-pt vol move — -0.006. Compare it against the main result of -0.001 /Δ/vol-pt before drawing conclusions.
Vanna-wealth per vol pt on 10 contracts — $-92.32 hedge-flow proxy. Compare it against the main result of -0.001 /Δ/vol-pt before drawing conclusions.
Current delta — 0.999. Compare it against the main result of -0.001 /Δ/vol-pt before drawing conclusions.
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.
How far Vanna can reasonably move
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 | Vanna per 1% vol |
|---|---|
| 80 % of the example value | -0.008 /Δ/vol-pt |
| 90 % of the example value | -0.003 /Δ/vol-pt |
| example inputs | -0.001 /Δ/vol-pt |
| 110 % of the example value | -0.000 /Δ/vol-pt |
| 120 % of the example value | -0.000 /Δ/vol-pt |
That spread — -0.008 /Δ/vol-pt at the low end, -0.000 /Δ/vol-pt at the high — is what a careful read of Vanna 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 Vanna
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the vanna per 1% vol recomputed, so the ranking below is measured rather than asserted. It is the fastest honest answer to “what matters most in Vanna?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Nudge Underlying price by ±10 % and Vanna lands between -0.003 /Δ/vol-pt and -0.000 /Δ/vol-pt (sensitivity ≈361.1 %)
- Strike +10 % → Vanna = -0.002 /Δ/vol-pt · −10 % → -0.000 /Δ/vol-pt (the vanna per 1% vol shifts ≈307.9 %)
- Implied volatility: ten percent up gives -0.001 /Δ/vol-pt, ten percent down gives -0.000 /Δ/vol-pt — ≈72.1 % of the vanna per 1% vol either way
- Time to expiry +10 % → Vanna = -0.001 /Δ/vol-pt · −10 % → -0.000 /Δ/vol-pt (the vanna per 1% vol shifts ≈35.1 %)
- Risk-free rate +10 % → Vanna = -0.001 /Δ/vol-pt · −10 % → -0.001 /Δ/vol-pt (the vanna per 1% vol shifts ≈4.0 %)
Underlying price is the dominant lever here: ten percent either way moves the result by about 361.1 %, from -0.003 /Δ/vol-pt to -0.000 /Δ/vol-pt. That is where a careless figure does the most damage, so check it against a source, and treat Strike as the second priority (≈307.9 % 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 Vanna of -0.001 /Δ/vol-pt means in practice
The value above only becomes useful the moment you know what it is being measured against. On the example inputs the band reads “Each implied-vol point shifts delta -0.0006 — a 5-pt IV spike re-hedges this position by -0.003 delta before the stock moves at all”; your own figures place you on a different rung of the same ladder. Before treating the band as fact, note its width: ten percent either way on Underlying price already spans -0.003 /Δ/vol-pt to -0.000 /Δ/vol-pt. 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.
Where Vanna sits next to similar measures: this tool answers “how much is the Vanna”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
How people get Vanna wrong
Vanna flows are conditional and reflexive — they amplify regimes, not predict them. Reading a single option’s vanna without the dealer’s net vanna positioning across the chain is the map that is not the territory. 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.
Reusing a Vanna from last season. In Investing & Markets the inputs are the thing that drifts; the formula does not.
This model has its own particular trap: Underlying price carries ≈361.1 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
Another is comparing across contexts: a Vanna 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.
Six things to confirm before acting on Vanna
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Re-verify Underlying price against a source document — ten percent of error there moves the headline by ≈361.1 %.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Confirm the example values are plausible for your own situation before replacing them.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
A routine for decision-grade Vanna
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 Vanna 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. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
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. Half of a good calculation is knowing which input you would hate to be wrong about.
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. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
Step 4 — ask what would have to be true. Take the result you want and work backwards through the inputs until you find the assumption that produces it; then decide honestly whether that assumption is defensible. Repeating a calculation with the same numbers proves only that the arithmetic is reliable — which is worth knowing.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the -0.001 /Δ/vol-pt output. Six months from now the context is what turns this figure into a trend. Most surprises in numbers are surprises about inputs, not about formulas.
Who actually uses Vanna — and when
Most Options & Derivatives disagreements are arithmetic disagreements in disguise. When Vanna per 1% vol of -0.001 /Δ/vol-pt 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. Re-running a number costs seconds; retracting a decision costs considerably more.
Used properly this is a five-minute filter that saves weeks. Compute Vanna, reject what fails, and only then bring in the expensive analysis for the survivors. A result worth acting on survives having its two shakiest inputs halved.
There is a personal-administration use people overlook: periodic self-checking. Vanna quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. Rounding early is the quietest way to introduce a permanent error.
The questions that come up most about Vanna
What affects Vanna the most?
Measured on this engine, Underlying price is the dominant lever: moving it ±10 % shifts the vanna per 1% vol across -0.003 /Δ/vol-pt to -0.000 /Δ/vol-pt — about 361.1 % of the headline, with Strike next at ≈307.9 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: strike or underlying price?
Underlying price, by a factor of about 1.2. Concretely: ten percent on Underlying price is worth ≈361.1 % of Vanna, the same nudge on Strike only ≈307.9 %. That ranking is re-computed for each page from that page’s own defaults.
What is a typical Vanna?
With the example inputs on this page the result is -0.001 /Δ/vol-pt, labelled “Each implied-vol point shifts delta -0.0006 — a 5-pt IV spike re-hedges this position by -0.003 delta before the stock moves at all”. “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 Vanna by hand?
Use the stated model — Vanna = ∂Δ/∂σ = −φ(d1)·d2/σ per vol point (closed form) — and substitute in the order the tool prints (it starts from Vanna = −φ(d1)·d2/(σ·100) per vol pt = -0.00058). On the example inputs the hand route lands on -0.001 /Δ/vol-pt, 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 Vanna if underlying price changes by 10 %?
On these inputs a ±10 % change in underlying price takes Vanna to -0.000 /Δ/vol-pt against the -0.001 /Δ/vol-pt example — around 361.1 % of the headline. The same test on every other field is in the sensitivity section.
Is the Vanna result of -0.001 /Δ/vol-pt good or bad?
The tool answers “what”, not “whether”: -0.001 /Δ/vol-pt carries the verdict “Each implied-vol point shifts delta -0.0006 — a 5-pt IV spike re-hedges this position by -0.003 delta before the stock moves at all” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Can I predict future returns with Vanna?
No tool predicts; Vanna computes implications. Use it to ask "if these inputs hold, what follows" — then stress the assumptions.
What affects Vanna the most?
Sensitivity depends on where you start, but the inputs Underlying price ($) and Strike ($) typically move Vanna further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
What is a vanna squeeze?
Vol dropping forces dealers long delta (short puts) to buy stock, which lowers vol further — a self-reinforcing melt-up.
Is vanna the same as volga?
No — volga is vega’s own curvature in vol; vanna is delta’s dependence on vol (spot × vol axis).
Does this Vanna tool store my numbers?
No. The entire calculation runs in your browser session; nothing entered above is transmitted or saved, which is the correct behaviour for sensitive Investing & Markets figures and the reason you can re-run this page as often as you like.
Key terms on this page
- Δ-shift on 5-pt vol move
- -0.003 for the Vanna worked case; it sits next to the main result because it carries context the headline leaves out.
- Δ-shift on 10-pt vol move
- -0.006 on the example inputs — a companion figure printed beside the headline of Vanna so that no result is read in isolation.
- Vanna-wealth per vol pt on 10 contracts
- $-92.32 hedge-flow proxy in the default Vanna calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Vanna per 1% vol
- The primary output of this tool: -0.001 /Δ/vol-pt for the default inputs, computed exactly from Vanna = ∂Δ/∂σ = −φ(d1)·d2/σ per vol point (closed form).
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The plain-language label — here “Each implied-vol point shifts delta -0.0006 — a 5-pt IV spike re-hedges this position by -0.003 delta before the stock moves at all” — mapping the computed figure onto experience-based ranges for Investing & Markets.
- Sensitivity (±10 %)
- How far the Vanna 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 Vanna model comes from
Everything above runs on one stated formula, applied without hidden coefficients: Vanna = ∂Δ/∂σ = −φ(d1)·d2/σ per vol point (closed form). Source of record: Dealer-flow literature; standard mixed derivative. 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.
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 Vanna into a decision
Save the number together with its inputs and today’s date; a Vanna figure without context is unusable the moment an input changes.
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.