The same logic can be applied to currency pairs in which the U.S. dollar is not one of the currencies. Either currency can be expressed in terms of the other. Intrinsic value is simply the difference between the spot price and the strike price. A put option will have intrinsic value only when the spot price is below the strike price. A call option will have intrinsic value only when the spot price is above the strike price.
Time value is more complex.
When the price of a call or put option is greater than its intrinsic value, it is because it has time value. Time value falls toward zero as the expiration date approaches. Another commonly used model for currency option valuation is the Garmen-Kohlhagen model. There are many texts available which cover the specifics of option pricing models in detail.