Explanation

Let's analyze the impact of dividends on different types of options:

Impact on Call Options:

• European call options: Dividends decrease the value because the stock price drops by the dividend amount on the ex-dividend date, reducing the potential upside.
• American call options: Dividends also decrease the value, and early exercise may be optimal just before ex-dividend dates to capture the dividend.

Impact on Put Options:

• European put options: Dividends increase the value because the stock price drop makes it more likely the put will be in-the-money.
• American put options: Dividends increase the value even more than European puts because early exercise opportunities become more valuable when dividends are present.

Now evaluating each option:

A: Incorrect - Dividends affect both European and American call options, reducing their value.

B: Incorrect - While dividends do increase the value of European put options, they also increase (not decrease) the value of American put options.

C: Incorrect - Dividends do decrease call option values, but American put options are affected by dividends (their value increases).

D: Correct - With dividends, American put options have higher value than without dividends due to additional early exercise opportunities around dividend dates.

Therefore, the correct answer is D