
Explanation:
The sensitivity of an option's price to a 1% change in volatility is measured by its Vega, multiplied by 0.01.
The formula for Vega is: .
Given , we find the standard normal inverse (z-score) is .
The probability density function value is .
Time to maturity in years , so .
Calculating Vega: $68.30 \times 0.5734 \times 0.3626 \approx 14.19814.19`8 \times 0.01 \approx 0.1420$. Option A (0.1424) is the closest approximation.
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Q.72 Consider a $75 call option on a non-dividend paying stock where the stock price is $68.30, the risk-free rate is 5%, the time to maturity is 120 days and N(d₁) = 0.3311. A 1% increase in the volatility will increase the value of the option by approximately:
A
0.1424
B
0.0743
C
0.1297
D
2.4873
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