i What this calculator does
Quick answer: Currency options are priced with the Garman-Kohlhagen model, which treats the base currency’s interest rate like a dividend yield; FX dealers quote them by volatility, risk reversal and butterfly rather than by price. With the default inputs the calculator returns premium: 10 446 USD.
A currency option gives the right to exchange one currency for another at a fixed rate on a future date. Because both currencies earn interest, the standard model, published by Mark Garman and Steven Kohlhagen in 1983, adjusts Black-Scholes with two interest rates: the quote currency’s as the risk-free rate and the base currency’s in place of a dividend. This calculator prices calls and puts on any pair, in pips and in money on your notional, with the Greeks, the forward rate and the probability of finishing in the money.
It also builds the volatility smile the way the interbank market quotes it: at-the-money volatility plus the 25-delta risk reversal and butterfly. From those three numbers it solves the 25-delta call and put strikes and reads the right volatility for any strike you enter. The equity version of the model is the Black-Scholes calculator.
This calculator is for educational purposes only. Results are estimates and may vary depending on market conditions, spreads, commissions, platform settings, and exchange rates. It should not be considered financial advice.
Common results
What the calculator returns as the days to expiry changes, with every other input at its default (currency pair EUR/USD, option type Call on the base currency, spot rate 1.16, quote currency interest rate 4, base currency interest rate 2, at-the-money volatility 8, 25-delta risk reversal -0.5, 25-delta butterfly 0.2).
| Days to expiry | Premium | Delta |
|---|---|---|
| 7 days | 5 090 USD | 0.500 |
| 14 days | 7 175 USD | 0.500 |
| 30 days | 10 446 USD | 0.499 |
| 60 days | 14 662 USD | 0.498 |
| 90 days | 17 847 USD | 0.498 |
| 180 days | 24 863 USD | 0.495 |
Why FX options need two interest rates
Holding the base currency earns its interest rate and holding the quote currency earns its rate, so the forward rate sits above or below spot by the interest differential. Garman-Kohlhagen discounts the spot leg at the base currency rate and the strike leg at the quote currency rate. When the quote currency pays more interest, as with USD/ZAR where rand rates are higher, the forward is above spot and calls on the base currency cost more than puts with the same strike. The forward rate calculator shows the same differential without the option.
Risk reversals and butterflies
Dealers quote FX options by volatility, not price. The at-the-money volatility sets the level. The 25-delta risk reversal is the volatility of a 25-delta call minus a 25-delta put: negative when the market pays more for protection against a fall in the base currency, as it usually does for emerging-market currencies against the dollar. The 25-delta butterfly is how much the two wings trade above at-the-money, the curvature of the smile. Together they let you read the market’s view of tail risk on any pair.
Delta, strikes and hedging
In FX, strikes are often chosen by delta rather than by price: a 25-delta call is the strike whose delta is 0.25. The calculator uses spot delta without premium adjustment, the convention for most pairs where the premium is paid in the quote currency. A delta of 0.50 on one million euros means the option behaves like 500,000 euros of spot, which is the amount a dealer would sell to hedge it. Gamma and vega show how fast that hedge and the premium change as spot and volatility move.
Spotted an outdated figure? If a rate, limit or formula in this calculator no longer matches its source, email us the page and the source. A material correction is dated on the Updates Log.
Frequently asked questions
What is the Garman-Kohlhagen model?
The standard model for pricing European currency options. It is Black-Scholes with the base currency’s interest rate in place of a dividend yield and the quote currency’s rate as the risk-free rate.
What is a 25-delta risk reversal?
The implied volatility of a 25-delta call minus that of a 25-delta put. Negative values mean puts on the base currency are in higher demand than calls.
What is a 25-delta butterfly?
The average volatility of the 25-delta call and put minus the at-the-money volatility. It measures how much the market pays for large moves in either direction.
Why are FX option premiums quoted in pips?
Because the premium is a price per unit of the base currency in the quote currency, like an exchange rate. On EUR/USD, 100 pips is 0.01 USD per euro, or 10,000 USD on one million euros.
What does at the money mean in FX?
Dealers usually mean the delta-neutral straddle strike, where a call and a put at the same strike have equal and opposite deltas. It sits slightly above the forward.
Can retail traders buy FX options?
Some brokers offer exchange-traded or OTC FX options to retail clients, but most retail forex is spot or CFD. The calculator is equally useful for understanding hedging costs quoted by banks.
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