How does the foreign interest rate enter the Garman-Kohlhagen model?

In Garman-Kohlhagen, the foreign currency acts like a dividend-paying asset. The foreign interest rate r_f is subtracted from the domestic rate r_d in the d1 formula: d1 = [ln(S/K) + (r_d - r_f + vol^2/2) x T] / (vol x sqrt(T)). Higher foreign rates reduce call option value and increase put option value.

What is FX implied volatility and how is it quoted?

FX implied volatility is quoted as annualized standard deviation of log returns, typically for 1-week to 1-year tenors. Delta-neutral straddle volatility is the benchmark; risk reversals capture smile asymmetry; butterfly spreads capture kurtosis. ATM FX vols range from 5–6% for EUR/USD to 20%+ for EM currency pairs.

FX Option Premium (Garman-Kohlhagen)

Calculate European FX option premium using the Garman-Kohlhagen model (Black-Scholes adapted for FX): incorporating spot rate, strike, domestic rate, foreign rate, time, and implied volatility.

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Frequently Asked Questions

How does the foreign interest rate enter the Garman-Kohlhagen model?

What is FX implied volatility and how is it quoted?