Explanation

Dividends have a significant impact on option values:

For call options:

• European call options: Dividends decrease the value because when a stock pays dividends, the stock price drops by the dividend amount, reducing the potential upside for call option holders.
• American call options: Dividends also decrease the value, and may lead to early exercise if the dividend amount exceeds the time value remaining in the option.

For put options:

• European put options: Dividends increase the value because the expected drop in stock price due to dividends makes put options more valuable.
• American put options: Dividends increase the value even more than European puts, as the option holder can exercise early to capture the dividend effect.

Analysis of each option:

• A: Incorrect - Dividends DO affect European call options (they decrease their value)
• B: Incorrect - While dividends increase European put value, they also INCREASE American put value, not decrease it
• C: Incorrect - While dividends decrease call option values, American put options ARE affected by dividends (their value increases)
• D: CORRECT - With dividends, American put options are more valuable than without dividends because the dividend payments create additional opportunities for profitable early exercise

The key insight is that dividends make American put options more valuable because they can be exercised early to capture the stock price drop that occurs when dividends are paid.