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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 This question deals with dividend sensitivity in the Black-Scholes model adjusted for dividends. **Key concepts:** - **Call options**: Decrease in value when dividends increase (dividends reduce stock price) - **Put options**: Increase in value when dividends increase (dividends reduce stock price, benefiting puts) - **Sensitivity**: Measured by rho (dividend sensitivity) **Why C is correct:** - **In-the-money options** have the highest absolute sensitivity to dividend changes because: - They have higher delta values - More of their value comes from intrinsic value, which is directly affected by stock price changes - Dividend payments reduce stock price, affecting intrinsic value more significantly - **Out-of-the-money options** have the lowest absolute sensitivity because: - They have lower delta values - Most of their value comes from time value, which is less affected by immediate dividend impacts **Why others are wrong:** - **A**: Incorrect - Out-of-the-money calls have lower sensitivity than in-the-money calls - **B**: Incorrect - The relationship isn't "always" larger; it depends on moneyness and other factors - **D**: Incorrect - At-the-money options don't have the largest sensitivity; in-the-money options do **Mathematical reasoning:** The dividend sensitivity (rho) in Black-Scholes is proportional to the option's delta. Since in-the-money options have deltas closer to ±1, they exhibit greater sensitivity to dividend changes than at-the-money or out-of-the-money options.
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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.