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Answer: Keeping the type of option constant, in-the-money options experience the greatest absolute change in value and out-of-the-money options the smallest absolute change in value as expected dividends increase.
## Explanation In the Black-Scholes model adjusted for dividends, the key insight is that **dividends reduce the stock price** when they are paid. This affects options differently: - **Call options**: Decrease in value when dividends increase (since the underlying stock price drops) - **Put options**: Increase in value when dividends increase (benefiting from the stock price drop) **Why option C is correct:** 1. **In-the-money options have the highest absolute sensitivity** because they have the highest delta (closest to 1 for calls, -1 for puts). The delta represents the sensitivity of option price to changes in the underlying stock price. 2. **Out-of-the-money options have the lowest absolute sensitivity** because their delta is close to 0, meaning they are less responsive to stock price changes caused by dividends. 3. **At-the-money options** have moderate sensitivity (delta around 0.5 for calls, -0.5 for puts). **Mathematical reasoning:** The sensitivity to dividends is proportional to the option's delta (∂V/∂S). Since in-the-money options have the highest absolute delta values, they experience the greatest absolute price changes when dividends affect the stock price. **Why other options are incorrect:** - **A**: Out-of-the-money calls actually have smaller decreases in value due to their lower delta - **B**: The relationship between put and call price changes isn't always consistent and depends on moneyness - **D**: At-the-money options don't have the largest absolute change; in-the-money options do
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Wanda Zheng (FRM) is responsible for the options desk in a London bank. Zheng is concerned about the impact of dividends on the options held by the options desk. She asks you to assess which options are the most sensitive to dividend payments. What would be your answer if the value of the options is found by using the Black-Scholes model adjusted for dividends?
A
Everything else equal, out-of-the-money call options experience a larger decrease in value than in-the-money call options as expected dividends increase.
B
The increase in the value of in-the-money put options caused by an increase in expected dividends is always larger than the decrease in value of in-the-money call options.
C
Keeping the type of option constant, in-the-money options experience the greatest absolute change in value and out-of-the-money options the smallest absolute change in value as expected dividends increase.
D
Keeping the type of option constant, at-the-money options experience the largest absolute change in value and out-of-the-money options the smallest absolute change in value as a result of dividend payment.