Answer: With dividends, the value of American put options exceeds the value without dividends.

## 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**

Author: LeetQuiz Editorial Team