reasons for the smile in fx options

[Adam]

In Section 20.2 in Hull (9th global), it is said that "As the maturity of the option is increased, the percentage impact of a nonconstant volatility on prices becomes more pronounced, but its percentage impact on implied volatility usually becomes less pronounced". Why is this the case? I would have thought non-constant vol would lead to bigger impact on price and implied vol for longer maturity.

 

[mugono]

In Section 20.2 in Hull (9th global), it is said that "As the maturity of the option is increased, the percentage impact of a nonconstant volatility on prices becomes more pronounced, but its percentage impact on implied volatility usually becomes less pronounced". Why is this the case? I would have thought non-constant vol would lead to bigger impact on price and implied vol for longer maturity.

I think you're over analysing this. Nevertheless, some comments:
1. The vega of an option (the impact on the price of an option for unit movement in implied volatility) increases as maturity increases.
2. The IV smile of an option tends to flatten as the time to expiry increases. The front of the curve is more sensitive to market sentiment: as you extend duration the impact in the short-term is 'averaged' out with the more benign / long-term reversion to the mean type dynamics.