Garman-Kohlhagen FX Put Price
Prices an FX put option with the Garman-Kohlhagen model, the currency-market version of Black-Scholes. As with the call, the foreign interest rate enters as a continuous dividend on the base currency: the premium is K·e^(−rd·T)·N(−d2) − S·e^(−rf·T)·N(−d1). The strike term is discounted by the domestic rate and the spot term by the foreign one. It's used to hedge against a currency falling or to speculate in that direction. 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 Put Price
Prices an FX put option with the Garman-Kohlhagen model, the currency-market version of Black-Scholes. As with the call, the foreign interest rate enters as a continuous dividend on the base currency: the premium is K·e^(−rd·T)·N(−d2) − S·e^(−rf·T)·N(−d1). The strike term is discounted by the domestic rate and the spot term by the foreign one. It's used to hedge against a currency falling or to speculate in that direction. Enter the spot rate, the strike, the domestic and foreign rates, the term in years and the volatility.
Insurance against a currency falling
Anyone who earns in dollars and pays bills in another currency, or the other way round, lives at the mercy of the exchange rate. An FX put option is the classic hedge against that risk: it locks in a conversion floor. If the currency plunges, the put gains value and offsets the loss; if it rises, the most you lose is the premium paid. The Garman-Kohlhagen model is what puts a price on this insurance.
The formula is the call's sibling: K·e^(−rd·T)·N(−d2) − S·e^(−rf·T)·N(−d1). The detail that defines the model is still there, in the foreign interest rate acting as a dividend on the base currency. The same golden rule applies: the strike is discounted by the domestic rate and the spot price by the foreign one. Swapping the two is the mistake that wrecks the calculation.
Enter the spot quote, the strike, both rates, the term in years and the FX volatility. The result is the theoretical premium of the protection. As with any Black model, it assumes constant volatility and European exercise, so use the number as a fair-price reference, not as the exact quote a desk would show.
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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.