Garman-Kohlhagen FX Call Price
Prices an FX call option with the Garman-Kohlhagen model, the extension of Black-Scholes to the currency market. The foreign interest rate behaves like a continuous dividend on the base currency: the premium is S·e^(−rf·T)·N(d1) − K·e^(−rd·T)·N(d2). The spot term is discounted by the foreign rate and the strike by the domestic rate — swapping the two flips the result. It is used for hedging and speculation with currency options. Enter the spot rate, the strike, the domestic and foreign rates, the term in years and the volatility.
Result
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Garman-Kohlhagen FX Call Price
Prices an FX call option with the Garman-Kohlhagen model, the extension of Black-Scholes to the currency market. The foreign interest rate behaves like a continuous dividend on the base currency: the premium is S·e^(−rf·T)·N(d1) − K·e^(−rd·T)·N(d2). The spot term is discounted by the foreign rate and the strike by the domestic rate — swapping the two flips the result. It is used for hedging and speculation with currency options. Enter the spot rate, the strike, the domestic and foreign rates, the term in years and the volatility.
Why an FX option needs its own formula
When the underlying is a currency, a wrinkle shows up that the stock version of Black-Scholes never accounts for: the foreign currency earns interest while you hold it. Mark Garman and Steven Kohlhagen sorted this out in 1983 by treating the foreign interest rate as a continuous dividend. That's why pricing a dollar option isn't the same exercise as pricing a stock option.
The premium comes from S·e^(−rf·T)·N(d1) − K·e^(−rd·T)·N(d2). Notice the symmetry: the spot term is discounted at the foreign rate and the strike at the domestic rate. Swapping one for the other is the classic mistake when someone codes the model in a hurry, and that alone flips the result. The interest-rate gap between the two countries is, in the end, what pushes the forward exchange rate up or down.
Enter the spot quote, the strike, both rates (domestic and foreign), the term in years and the FX volatility. It works equally well for an exporter wanting to lock in a price and for someone just studying how the currency-options market behaves. The figure is theoretical and European, so take it as a reference.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.