How does increasing time to maturity affect foreign currency option value?

What will be an ideal response?

Here, it is important to distinguish clearly between American-style and European-style options. For American options, the effect is unambiguous: Increasing the time to maturity always increases an option's value because it increases the uncertainty of the spot exchange rate at maturity. When this effect is combined with the fact that the holder of a 6-month option can always treat the option as a 3-month option, we clearly see that the additional 3 months of maturity cannot hurt the payoff to the holder of the option as long as the holder of the option can exercise it early.
For European options, the situation is not so simple. Although the effect of an increase in time to maturity is technically ambiguous, in most situations, the effect of the increased uncertainty of the spot exchange rate at maturity dominates, and option prices increase. Nevertheless, this is not always true because it is possible for a European option that is currently in the money to lose value as time evolves. You would like to be able to exercise the option to lock in the revenue now, but you cannot do so prior to maturity.