Currency Option Implied Volatility Calculator
Solve the constant annualized volatility that makes a Garman-Kohlhagen European currency-option model match one entered premium. The calculation uses entered spot, strike, continuously compounded quote- and base-currency rates and time; it does not connect to an option chain or construct a volatility surface.
Enter one currency-option premium
Use quote currency per one base currency for spot, strike and premium per base unit. Keep the rate orientation consistent with the currency pair.
Entered-premium model-implied volatility
Derived from FX Option Quote Conventions model 1.0.0.
How the entered-premium implied volatility is solved
Implied volatility is not entered directly on this route. The calculator repeatedly reprices the selected European call or put and searches for the annualized volatility that makes the model premium equal the premium entered by the user. Version 1.0.0 uses a bounded bisection solver from 0.0001% through 1000%.
Garman-Kohlhagen discounts both currencies. With the page convention of quote currency per one base currency, the quote-currency rate is the domestic rate and the base-currency rate is the foreign rate. Swapping the two rate labels without also reversing spot and strike describes a different contract.
The entered premium is quote currency per one base-currency unit. A premium of 0.03246893 on EUR/USD means USD 0.03246893 per EUR of option notional. The page deliberately avoids assuming a universal 100,000-unit lot, contract multiplier or total cash premium.
For a valid plain-vanilla European option case, theoretical premium rises with volatility, allowing bisection to bracket one solution. If the entered premium falls outside the model prices at the disclosed volatility bounds, the page withholds a result instead of forcing a number.
The same premium can imply different volatility when spot, strike, rates, time basis, exercise style or quote convention changes. The result is therefore meaningful only with the exact contract inputs and timestamp associated with the premium.
Real FX option markets commonly quote volatility by tenor and delta and may use pair-specific delta, ATM and butterfly conventions. One inverted premium is a single point under one constant-volatility model; it does not recreate those conventions or an arbitrage-free smile.
Worked example from the audited fixture
The audited fixture enters a EUR/USD call with spot 1.10000, strike 1.12000, 4% USD quote-currency continuous rate, 2% EUR base-currency continuous rate and 180 days on a 365-day basis.
The entered premium is USD 0.0324689310779 per EUR. Bisection finds 12.0000% annualized volatility and reprices the premium to the same value within the displayed numerical residual.
At the solved volatility, the unadjusted call spot delta is 0.47351773, vega is USD 0.00304692 per EUR for one volatility point and the continuous-rate forward is 1.11090299.
How to interpret the result
- Call the output entered-premium model-implied volatility, not live implied volatility, because the page receives no option chain or timestamped dealer quote.
- Check the premium unit first. A total cash premium, percentage-of-notional quote or premium in the base currency must be converted from a confirmed contract specification before entry.
- Confirm that both rates are continuously compounded annual rates for the same horizon and currency orientation as spot and strike.
- Use the premium residual to confirm numerical convergence; it does not measure pricing error against the market.
- Treat delta and vega as local model diagnostics at the solved point, not hedge instructions or guaranteed price changes.
- Compare multiple premiums only when their exercise style, expiry cut, settlement, notional and quotation conventions are consistent.
Which FX option quote-convention tool answers which question?
These tools share one governed model layer but solve different inverse problems. Premium inversion finds volatility, delta inversion finds strike, and RR/BF conversion rearranges volatility quotes without pricing an option.
| Tool | Required entered data | Output | Hard boundary |
|---|---|---|---|
| Implied volatility | Premium plus spot, strike, two rates and time | One constant volatility | Does not build a surface |
| Delta-to-strike | Spot, two rates, volatility, time and delta | One strike | Unadjusted spot delta only |
| Risk reversal & butterfly | ATM plus RR/BF or two wing volatilities | Volatility quote conversion | Simple average BF; no strikes |
Assumptions and limitations
- No live spot, yield curve, option chain, bid, ask, mid, volatility surface, broker account, order or contract record is connected.
- The underlying model assumes European exercise, lognormal spot, constant volatility and continuously compounded constant rates through the entered horizon.
- Early exercise, barriers, digitals, Asians, path dependence, stochastic volatility or rates, jumps, credit, collateral and liquidity adjustments are excluded.
- Smile interpolation, delta conventions, ATM definitions, premium adjustment and pair-specific market conventions are not inferred.
- The searched volatility interval is 0.0001% through 1000%. A premium outside the corresponding model-price bracket is withheld.
- No option, volatility, strike, premium, hedge, provider, broker, strategy, signal, valuation conclusion or trade is recommended.
Sources and methodology
The arithmetic is independently fixture-tested. These primary and implementation references define the formulas and convention distinctions; they do not verify an entered premium, quote, contract, provider or market timestamp.
- LCH — Options Valuation Formulas — Primary clearing methodology documenting Garman-Kohlhagen currency-option valuation and Greeks.
- Garman and Kohlhagen — Foreign Currency Option Values — Bibliographic record for the original two-interest-rate currency-option model.
- FX Options Pricing with Market Conventions — Peer-reviewed discussion of volatility quotation and FX-specific delta and smile conventions.
Frequently asked questions
- It solves the constant annualized volatility that makes the disclosed Garman-Kohlhagen model equal one entered call or put premium.
- No. The premium and every other input are entered manually, and no option chain or market timestamp is connected.
- A currency pair contains two currencies, so Garman-Kohlhagen discounts the base and quote currency legs separately.
- Enter quote currency per one base-currency unit, on the same orientation as spot and strike.
- The premium may lie outside the prices produced across the disclosed 0.0001% to 1000% volatility range for the entered case.
- No. It solves one constant-volatility point and does not interpolate across strikes, deltas or expiries.
- No. Version 1.0.0 is limited to plain-vanilla European call and put arithmetic.
- No. It is conditional model output, not a forecast, valuation conclusion or recommendation.
Separate premium inversion from pricing and quote conversion
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