Currency Option Pricing Calculator

How the Garman-Kohlhagen currency-option estimate is calculated

The quote convention is locked as quote currency per one base-currency unit. In EUR/USD at 1.1000, EUR is the base currency and USD is the quote currency. The quote-currency rate is the domestic rate in the formula; the base-currency rate is the foreign rate. Reversing the exchange-rate quote without also reversing the rates and strike describes a different contract.

Garman-Kohlhagen adapts the European Black-Scholes framework to a currency pair by discounting both currencies. The base-currency rate behaves like a continuous yield on the underlying base currency, while the quote-currency rate discounts the strike payment. Both rates on this page are entered continuously compounded annual rates rather than simple money-market rates or APYs.

Annualized volatility is an assumption, not a measured result on this route. A professional FX option quote may depend on tenor, strike or delta, currency-pair conventions and a volatility smile or surface. Entering one flat volatility produces one constant-volatility scenario and does not reveal the market-implied volatility that would match a dealer premium.

The model prices European exercise at the entered expiry horizon. It does not price American early-exercise rights, barriers, digitals, Asians, average-rate structures, knock-ins, knock-outs or other path-dependent contracts. Contract style, fixing, cash versus physical settlement and automatic-exercise rules must be checked independently.

The direct base-currency notional multiplies the per-unit premium. The page does not assume a 100,000-unit forex lot or an exchange contract multiplier. CME, OTC and broker products can use different notionals, premium quotations, ticks, deliverables and settlement procedures, so a user must translate the actual contract specification before comparing amounts.

Delta, gamma and vega are local model sensitivities, not guaranteed changes or hedge instructions. Delta uses the spot convention in this model, gamma is per one spot-rate unit, and vega is shown for a one-percentage-point volatility change. Large moves and assumption changes require full repricing rather than linear sensitivity multiplication.

Worked example from the audited fixture

The audited fixture enters EUR/USD spot and strike at 1.10000, a 5% USD quote-currency continuous rate, a 3% EUR base-currency continuous rate, 10% annualized volatility, 180 days on a 360-day basis and EUR 100,000 notional.

1. Time is 0.5 years, d1 is 0.17677670 and d2 is 0.10606602. The continuous-rate forward is 1.11105518 and the theoretical call premium is 0.03610461 USD per EUR.
2. The call total is USD 3,610.46 and the put total is USD 2,532.24. Selected call delta is 0.56166955, total vega for one volatility point is USD 300.95 and the computed put-call parity gap rounds to zero.

Reproduce it: select “Load audited example” above. The immutable fixture is recomputed from the disclosed equation rather than copied from a provider result.

How to interpret the result

• Read the premium as conditional model output under every entered assumption. It is not an executable bid, ask, mid, settlement price, dealer valuation or statement that an option is cheap or expensive.
• Confirm that the spot, strike and both rates use the same base/quote orientation. A plausible-looking result can still be economically reversed if domestic and foreign labels are swapped.
• Use a volatility input for the exact pair, expiry and strike or delta convention only when its source and timestamp are known. Historical volatility and implied volatility answer different questions and are not interchangeable.
• Treat delta, gamma and vega as local diagnostics. They do not include smile dynamics, transaction costs, discrete hedging, gaps, liquidity, funding or the effect of changing more than one input simultaneously.
• Check the model call-minus-put result against the disclosed discounted spot-minus-strike parity reference. A tiny floating-point gap is expected; a material gap indicates inconsistent inputs or implementation.
• Compare with a real contract only after confirming exercise style, expiry and cut time, fixing, settlement, notional, premium currency, quote convention and whether the underlying is spot, futures or another instrument.

Assumptions and limits

• No live spot, option chain, implied-volatility surface, yield curve, broker account, exchange account, dealer quote, contract, order, exercise, assignment or settlement system is connected.
• The model assumes lognormal spot, constant volatility, constant continuously compounded rates, frictionless trading and no default. Real prices can depart materially from those assumptions.
• European exercise only is supported. American, Bermudan, barrier, digital, Asian, quanto, compound, cancellable and other structured options are excluded.
• The single entered volatility does not model smile, skew, term structure, stochastic volatility, jumps or liquidity. The page does not solve implied volatility from an entered market premium.
• Greeks are analytical spot-model sensitivities. Premium-adjusted, forward and market-delta conventions, sticky-strike or sticky-delta rules and hedge execution are excluded.
• No option, strike, tenor, volatility, provider, broker, direction, hedge, exercise decision, strategy, signal or trade is recommended.

Sources and methodology

• Garman and Kohlhagen — Foreign Currency Option Values — Original research reference for the two-rate European currency-option framework.
• LCH SA — Options Valuation Formulas — Clearing-methodology reference for Garman-Kohlhagen-type currency-option premium and delta equations.
• CME Group — Listed FX Options — Professional reference for premium-per-base-unit, contract notional, call/put rights and contract-specific conventions.

Version 1.0.0 performs deterministic local arithmetic and uploads no entered value. Sources define option pricing, premium, contract and market boundaries; they do not verify an input, volatility, rate, premium, contract, provider quote, exercise, settlement or result.