Explanation:

The smallest increase in option value comes from doubling the riskfree rate.

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.

A) Double the riskfree rate (from 3.0%) to 6.0%

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:

$S(0) = K = \`$ 100.00` $and this option has a delta,$ N(d_1) = 0.570$

Volatility, $\sigma = 20.0\%$ and this option has vega = 27.8

Riskfree rate, $R_f = 3.0\%$

Time to expiration, $T = 0.5$ years or six months

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?

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MManit

Last updated: April 18, 2026 at 11:32

Double the riskfree rate (from 3.0%) to 6.0%

100.0%

Increase the stock price by $5.00 (from $100.00) to $105.00

0.0%

Increase volatility by 10.0% (from 20.0%) to 30.0%

Double the time to expiration (from six months) to $T = 1.0$ year

Financial Risk Manager Part 1