FX options

Garman-Kohlhagen prices and Greeks for FX calls and puts. Enter spot, strike, volatility, and the foreign (base) and domestic (quote) rates, then calculate.

The model is Black-Scholes for a currency pair such as EURUSD: the foreign (base) rate acts like a continuous yield on the spot, and the domestic (quote) rate discounts the strike. Use it for a European vanilla on an FX rate. Figures are theoretical and for information only.

Choose a pair to fill spot (domestic per one foreign), ~30-day historical realized vol, and the two interest-rate proxies (foreign/base and domestic/quote). Leave on Manual entry to type everything yourself. Strike is recentered near the new spot.

Garman–Kohlhagen: for pair XXXYYY (e.g. EURUSD), Foreign = first (XXX / base), Domestic = second (YYY / quote). Foreign rate = XXX interest rate; Domestic rate = YYY interest rate.

Delayed/free data. Historical realized vol is not implied vol from an options chain. Rate proxies are overnight or policy rates, not a dealer curve. Not investment advice.

Usual market quote: domestic (quote) currency per one unit of foreign (base).

Call and put results

Metric Call Put
Option Price — —
Delta — —
Gamma — —
Vega — —
Theta — —
Rho — —

How the Garman-Kohlhagen price is calculated

Garman-Kohlhagen extends Black-Scholes to a currency pair by using two rates. The foreign rate (base / first of XXXYYY) discounts the spot (as a continuous yield would); the domestic rate (quote / second of XXXYYY) discounts the strike. Volatility is still a single flat number, and exercise is only at expiry.

Time is a year-fraction T equal to days until expiration divided by 365. Rates and volatility are entered as percentages and converted to decimals. N is the standard normal cumulative distribution:

C = S e−rf T N(d1) − K e−rd T N(d2)

P = K e−rd T N(−d2) − S e−rf T N(−d1)

d1 = [ln(S / K) + (rd − rf + σ2 / 2) T] / (σ √T)

d2 = d1 − σ √T

  • S — FX spot rate (domestic per one foreign)
  • K — strike
  • σ — volatility (decimal)
  • rd — domestic interest rate of the quote currency (second of XXXYYY, e.g. USD in EURUSD)
  • rf — foreign interest rate of the base currency (first of XXXYYY, e.g. EUR in EURUSD)
  • T — time to expiry in years (days ÷ 365)

Option prices are rounded to three decimals, matching the results panel. Vega and rho are reported per one percentage point; theta is per calendar day. Rho is with respect to the domestic (quote) rate.

Worked examples

These three cases use the same formula and rounding as the calculator above. Type the inputs in and you should get the same call and put prices.

In-the-money call (defaults)

Spot 1.25, strike 1.10, 20% volatility, 2% domestic (quote) / 1% foreign (base), 365 days.

Call price
0.193
Put price
0.034
Call delta
0.77718

At-the-money, 20% vol

Spot and strike 1.10, same 20% vol and 2% domestic (quote) / 1% foreign (base) rates, 365 days. Call and put are closer once the option is no longer in the money.

Call price
0.092
Put price
0.081
Call delta
0.55405

ATM at 30% volatility

Spot and strike 1.20, 30% vol, 3% domestic (quote) / 1% foreign (base), 365 days. Higher vol lifts both premiums.

Call price
0.152
Put price
0.129
Call delta
0.57994

If the underlier is an equity-style spot with one rate, use the vanilla Black-Scholes tool. Implied volatility inverts that formula; the converter rescales a vol before you type it here.

Vanilla / binary options

Black-Scholes prices and Greeks for European calls, puts, and binaries.

Open calculator

Implied volatility

Back out Black-Scholes implied vol from an observed vanilla price.

Open calculator

Volatility converter

Translate daily, weekly, monthly, or annual volatility figures.

Open calculator

Value at Risk

Estimate theoretical maximum loss at a chosen confidence level.

Open calculator

FX option FAQ

Garman-Kohlhagen is Black-Scholes for a currency pair. The foreign interest rate (base currency, first of XXXYYY) plays the role of a continuous dividend yield: the spot is discounted at the foreign rate, and the strike is discounted at the domestic rate (quote currency, second of XXXYYY). There is still a single flat volatility and European exercise only.

For pair XXXYYY (e.g. EURUSD), Foreign is the first currency (XXX, the base) and Domestic is the second (YYY, the quote). The foreign rate is the interest rate of that foreign/base currency; the domestic rate is the interest rate of the domestic/quote currency. Spot is the usual market quote: domestic per one unit of foreign. Swapping the two rates changes both the forward and the price.

Yes. Exercise is at expiry only. American FX options, barriers, and first-generation exotics are not priced here. For an equity-style underlier with a single rate, use the vanilla / binary options calculator.

Enter calendar days. The model divides by 365 to get a year-fraction, so 365 days is exactly one year. There is no business-day calendar or market day-count switch.

Delta is the change in option value for a one-unit move in the FX spot, already multiplied by the foreign (base) rate discount. Gamma is the change in that delta. Vega and rho are scaled per one percentage point; theta is per calendar day. Rho is taken with respect to the domestic (quote) rate.

FX markets quote volatility by delta and tenor, not a single flat vol. Premiums may be in domestic (quote) or foreign (base) pips, and there are bid-ask spreads and smile adjustments. Rounding and the 365-day year can also differ. Figures here are theoretical and for information only.

Disclaimer: the contents of this website are for informational purposes only and do not constitute any investment recommendation. The visitor acts at his own risk.