Garman-Kohlhagen (GK) is the standard model used to calculate the price of an FX option, however there are a wide range of techniques in use for calculating the options risk exposure, or greeks. Although the price produced by every model will agree, the risk numbers calculated by different models can vary significantly depending on the assumptions used for the properties of the spot price movements, volatility surface and interest rate curves.
After GK, the most common models in use are SABR and local volatility, although when agreeing risk numbers with a counterparty (e.g. for exchanging delta, or calculating the strike on a 25 delta option) the Garman-Kohlhagen numbers are always used.
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