Put option question

CFA Level I
#1

Which of the following statements best describes a feature of an American option? Early exercise of an American:

  1. put option is optimal only if the underlying is dividend paying.
  2. call option is never optimal if the underlying is dividend paying.
  3. put option that is deep in the money may be optimal

Answer is 3, but It could also be 1, right? exercise early, before they pay the dividend, because if they pay the dividend and you have the put option, the underlying asset will go down and the value of your option to.

#2

Two problems with answer 1 and your analysis:

  • It says that early exercise is optimal _ only _ if the underlying pays a dividend. It may be optimal for options deep in the money whether the underlying pays a dividend or not.
  • When the price of the underlying decreases (e.g., ex-dividend), the value of a put option _ increases _; it doesn’t decrease.