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Answer: Double the riskfree rate (from 3.0%) to 6.0%
The **smallest** increase in option value comes from **doubling the riskfree rate**. ### Why? For a European call on a non-dividend-paying stock: - **Higher stock price** increases the call value by approximately **delta × change in stock price**. - Approximate change: \(0.570 \times 5 = 2.85\) - **Higher volatility** increases the call value by approximately **vega × change in volatility**. - Since vega is 27.8 and volatility rises by 0.10, approximate change: \(27.8 \times 0.10 = 2.78\) - **Higher interest rates** increase call value, but the effect is usually smaller than the stock-price or volatility effects here. - **More time to expiration** also increases call value, and for this near-the-money option it is likely to have a noticeable effect. Using Black-Scholes intuition, the rate increase from 3% to 6% produces the smallest change among the four choices. ### Correct answer **A) Double the riskfree rate (from 3.0%) to 6.0%**
Author: Manit Arora
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Question-725.1. Consider a European call option on a non-dividend-paying stock that has a current price, c = \`6.37`$, if we make the following assumptions:
Each of the following changes will INCREASE the value of this option, but which factor change will produce the SMALLEST change to the option’s value?
A
Double the riskfree rate (from 3.0%) to 6.0%
B
Increase the stock price by $5.00 (from $100.00) to $105.00
C
Increase volatility by 10.0% (from 20.0%) to 30.0%
D
Double the time to expiration (from six months) to year
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