Currency Option Premium Calculator
The formula
What the fx option premium tells you
Garman-Kohlhage extends Black-Scholes with two interest rates — the only way to honestly price currency options, because every FX claim straddles a rate differential on both legs.
Calculation: Garman-Kohlhage: C = S·e^(−rfT)N(d1) − K·e^(−rdT)N(d2), d1 with interest-rate differential. Enter your inputs and every substitution is shown below the result.
Reading the result
FX vol (10%) is roughly 2–3× equity vol but on a pair that barely trends — optionality on a nearly-martingale process: sellers collect, buyers insure.
Rules of thumb: ATM EURUSD 90-day straddle ≈ 0.9–1.6% of notional; risk reversals 2–6 vol points wide
Limitations and best practice
Quoting conventions (premium in % of notional vs per unit, points of spot) differ between desks — and risk-reversal pricing (put vol ≠ call vol) breaks the flat-vol premium by 10–20%.
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 two discount rates?
What is a risk reversal?
Why so much flatter vol in FX?
Source & methodology
Garman & Kohlhagen (1983), J. Intl Money & Finance.
How Currency Option Premium works — and what your result really means
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Currency Option Premium 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 Option premium in real time, and see every substitution printed below.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Currency Option Premium is on the table, the argument can stop being about impressions.
What makes Currency Option Premium worth calculating is not precision but position: it tells you which side of a threshold you are on, and by how much. A rough figure that settles the direction beats an elaborate one that never commits.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here option premium = 0.032 per unit, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Spot first, at ≈273.1 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
Inside the Currency Option Premium calculation: formula and every input
Here is the complete model this tool runs — Garman-Kohlhage: C = S·e^(−rfT)N(d1) − K·e^(−rdT)N(d2), d1 with interest-rate differential — 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.
Spot (per 1 EUR, $) (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. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
Strike (example value 1) is a plain measured quantity — the unit shown in the label is the unit the formula expects. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Days to expiry (example value 165) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Use the value as of today, not as of the last time you looked — time fields drift silently.
USD 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.
EUR rate (%) (example value 2) is a quantity rather than a category — precision here is cheap and worth having. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
FX volatility (%) (example value 9) is a measured number in the unit named by the label; the formula does not convert for you. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Type (example value Call (EUR)) is a selector, not a measurement: the engine follows a different route for each option. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
What each “Type” choice actually does: Call (EUR) → 0.032 per unit · Put (EUR) → 0.022 per unit These figures are computed from this engine, not estimated — switch the dropdown above and you will land on exactly these numbers.
Currency Option Premium on the example inputs: the complete substitution
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Spot (per 1 EUR, $), Strike, Days to expiry, USD rate (%). Run to the end, the option premium resolves to 0.032 per unit — At 2.94% of spot for 165 days, expensive: the market sees vol in this pair on the bands this tool uses.
- d1 = [ln(S/K) + (rd−rf+σ²/2)T]/(σ√T) on the GK model
- C = S·e^(−rfT)N(d1) − K·e^(−rdT)N(d2) = 0.0317 per unit
- On €1M notional: $31,675 for 165 days of protection
Forward (CIP) — 1.066 per unit. Compare it against the main result of 0.032 per unit before drawing conclusions.
Premium per €1M notional — $31,675. If your inputs change, this is usually the first companion figure to move.
Breakeven spot at expiry — 1.112. Compare it against the main result of 0.032 per unit before drawing conclusions.
Premium as % of spot — 2.94%. This is the number experienced users quote when the headline alone would mislead.
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.
The Currency Option Premium corridor: your result across a realistic band
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Currency Option Premium, not an interpolation.
| Spot setting | Option premium |
|---|---|
| 80 % of the example value | 0.000 per unit |
| 90 % of the example value | 0.002 per unit |
| example inputs | 0.032 per unit |
| 110 % of the example value | 0.118 per unit |
| 120 % of the example value | 0.224 per unit |
The corridor runs from 0.000 per unit to 0.224 per unit across that band — which is the range worth planning inside rather than the single 0.032 per unit point estimate. Reproduce it in the form above by editing Spot alone; the substitution steps will follow your figures exactly.
The levers behind Currency Option Premium, ranked by effect
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the option premium recomputed, so the ranking below is measured rather than asserted. For Currency Option Premium the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Nudge Spot by ±10 % and Currency Option Premium lands between 0.002 per unit and 0.118 per unit (sensitivity ≈273.1 %)
- Nudge Strike by ±10 % and Currency Option Premium lands between 0.003 per unit and 0.117 per unit (sensitivity ≈268.3 %)
- FX volatility: ten percent up gives 0.034 per unit, ten percent down gives 0.029 per unit — ≈8.2 % of the option premium either way
- Days to expiry +10 % → Currency Option Premium = 0.034 per unit · −10 % → 0.030 per unit (the option premium shifts ≈6.2 %)
- Nudge USD rate by ±10 % and Currency Option Premium lands between 0.031 per unit and 0.033 per unit (sensitivity ≈3.8 %)
- EUR rate +10 % → Currency Option Premium = 0.031 per unit · −10 % → 0.032 per unit (the option premium shifts ≈1.8 %)
Spot is the dominant lever here: ten percent either way moves the result by about 273.1 %, from 0.002 per unit to 0.118 per unit. That is where a careless figure does the most damage, so check it against a source, and Strike is effectively tied with it (≈268.3 % for the same nudge), so verify the pair together. 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 Currency Option Premium of 0.032 per unit means in practice
Nobody acts on a bare figure — they act on a figure with a comparison attached. On the example inputs the band reads “At 2.94% of spot for 165 days, expensive: the market sees vol in this pair”; your own figures place you on a different rung of the same ladder. How much of that band is luck? On Spot alone ten percent either way covers 0.002 per unit to 0.118 per unit. 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.
Related measures answer related questions, and the distinctions matter: Currency Option Premium is the quantity, Option premium is this tool’s reading of it, and the decision that follows belongs to neither of them separately.
Common mistakes with Currency Option Premium (and the fix)
Quoting conventions (premium in % of notional vs per unit, points of spot) differ between desks — and risk-reversal pricing (put vol ≠ call vol) breaks the flat-vol premium by 10–20%. 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.
Copying a single headline number without checking the companion outputs. The tool reports Forward (CIP), Premium per €1M notional and Breakeven spot at expiry alongside the main result precisely because Currency Option Premium in isolation misleads — the secondary columns are where outliers and trade-offs show up.
This model has its own particular trap: Spot carries ≈273.1 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
Another is comparing across contexts: a Currency Option Premium 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.
Currency Option Premium verification checklist
- Check whether the formula treats your inputs as nominal or real dollars.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Put Spot under a magnifier; the sensitivity table above is the reason why.
- Confirm rate conventions (APR vs effective, day-count) before comparing two offers.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
Step by step: getting a trustworthy Currency Option Premium 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 Currency Option Premium takes a minute to learn and applies to every input above.
Step 1 — collect, then type. Everything this tool asks for is listed above (spot (per 1 eur, $), strike, days to expiry, usd rate (%), eur rate (%), fx volatility (%) and the remaining fields listed above). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. Rounding early is the quietest way to introduce a permanent error.
Step 2 — baseline before exploration. Get one defensible Option premium on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. A figure nobody can reproduce is a figure nobody will act on twice.
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. When two sources disagree, it is almost never the arithmetic that differs.
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. Note the assumption you are least sure about; that is where the real risk lives.
Step 5 — write the one-line memo. “Option premium = 0.032 per unit 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. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
The real-world conversations Currency Option Premium settles
Finance & Banking arguments end at arithmetic or they do not end. Currency Option Premium is the arithmetic: 0.032 per unit on the example inputs, reproducible by anyone who types the same numbers. Rounding early is the quietest way to introduce a permanent error.
Used properly this is a five-minute filter that saves weeks. Compute Currency Option Premium, reject what fails, and only then bring in the expensive analysis for the survivors. Write the figure down before moving on; memory flatters whichever number you saw last.
There is a personal-administration use people overlook: periodic self-checking. Currency Option Premium 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. The inputs are the part of the work that nobody else can do for you.
Quick answers: what searchers ask about Currency Option Premium
What affects Currency Option Premium the most?
Currency Option Premium is driven above all by Spot. Perturbing only that field by ten percent either way produced 0.118 per unit against the 0.032 per unit baseline — a ≈273.1 % response, while Strike manages ≈268.3 %.
Do strike and spot matter equally?
On these inputs, yes: the two measured within a rounding error of each other — ≈273.1 % and ≈268.3 % of the option premium per ten-percent change. Treat them as one pair to verify together rather than ranking them.
How much does the “Type” choice change the answer?
The spread is not cosmetic: this choice alone takes Currency Option Premium from 0.022 per unit to 0.032 per unit with every other input frozen, which is more influence than most of the numeric fields on this page can claim.
What is a typical Currency Option Premium?
With the example inputs on this page the result is 0.032 per unit, labelled “At 2.94% of spot for 165 days, expensive: the market sees vol in this pair”. “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 Currency Option Premium by hand?
Use the stated model — Garman-Kohlhage: C = S·e^(−rfT)N(d1) − K·e^(−rdT)N(d2), d1 with interest-rate differential — and substitute in the order the tool prints (it starts from d1 = [ln(S/K) + (rd−rf+σ²/2)T]/(σ√T) on the GK model). On the example inputs the hand route lands on 0.032 per unit, 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 Currency Option Premium if spot changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 0.002 per unit to 0.118 per unit across the ten-percent probe, i.e. ≈273.1 % sensitivity on the option premium.
Is the Currency Option Premium result of 0.032 per unit good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Currency Option Premium sit against the 0.032 per unit reference above, how far would a plausible input error move it (≈273.1 % per ten percent on Spot), and what does the alternative option compute to?
How often should I check Currency Option Premium?
Whenever an input changes by more than a few percent, and otherwise on the rhythm of your decisions — before a purchase, a review, a renewal. Currency Option Premium is a snapshot, not a subscription; stale snapshots are the most common silent error in Finance & Banking planning.
Can Currency Option Premium be negative or empty?
Yes, and that is informative rather than broken: a negative Currency Option Premium usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
Why two discount rates?
The underlying "pays a dividend" — the foreign rate — so the spot is discounted at rf and the strike at rd.
What is a risk reversal?
Buy an OTM put, fund it with an OTM call — prices skew directly and is how corporates buy crash insurance cheaply.
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
- Forward (CIP)
- 1.066 per unit in the default Currency Option Premium calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Premium per €1M notional
- $31,675 in the default Currency Option Premium calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Breakeven spot at expiry
- 1.112 in the default Currency Option Premium calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Option premium
- The primary output of this tool: 0.032 per unit for the default inputs, computed exactly from Garman-Kohlhage: C = S·e^(−rfT)N(d1) − K·e^(−rdT)N(d2), d1 with interest-rate differential.
- 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 “At 2.94% of spot for 165 days, expensive: the market sees vol in this pair” — mapping the computed figure onto experience-based ranges for Finance & Banking.
- Sensitivity (±10 %)
- How far the Currency Option Premium moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
The provenance of this Currency Option Premium calculation
There is no black box on this page — the engine evaluates Garman-Kohlhage: C = S·e^(−rfT)N(d1) − K·e^(−rdT)N(d2), d1 with interest-rate differential. Source of record: Garman & Kohlhagen (1983), J. Intl Money & Finance. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. The sensitivity table above is part of that promise rather than a bonus: it lets you see how much of the result depends on how carefully you measured.
Turning this Currency Option Premium into a decision
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
The audience here is people who need one trustworthy number before their next decision. Everything you need to defend the result — formula, substitution, sensitivity, source — is printed above, so the only remaining variable is the honesty of your inputs.