Consider the following statements about currency options (note, OTM = out-of-the-money):

(i) An American put option is always worth zero if it is deeply OTM.

(ii) The time-value of an American call option is usually highest when the underlying spot price is trading close to the options exercise price.

(iii) If the current exercise price of a 3-month OTM American call option is below the 3- month forward exchange rate (on the same underlying currency pair), then the minimum price of the option is its intrinsic value.

(iv) The price of a European put option increases as the spot rate falls.

Which of the above statements are false?