Alpha stock is currently trading at $34.50 a share and the 6-month call options are at the money.The stock returns have a standard deviation of 21 percent and the risk-free rate is 4.21 percent.What is the price of the call option per share given that N(d₁)is .585508 and N(d₂₎ is .526913? A)$1.07 B)$2.79 C)$1.38 D)$2.40 E)$1.64

Question

Quizplus · Accepted Answer

Firstly, we can derive the components in the Black-Scholes formula using the given information:
- S = $34.50 (current stock price)
- K = $34.50 (strike price of the call option)
- T = 0.5 (6 months = 0.5 years)
- r = 4.21% (risk-free rate)
- σ = 21% (standard deviation of stock returns)

Using these inputs, we can calculate d1 and d2:
d1 = [ln(S/K) + (r + (σ^2)/2)T] / (σ√T) = 0.0789
d2 = d1 - σ√T = -0.2386

Next, we plug these into the Black-Scholes formula:
Call price per share = SN(d1) - Ke^(-rT)N(d2)
= $34.50(0.585508) - $34.50e^(-0.0421*0.5)(0.526913)
= $2.40

Therefore, the correct answer is (D) $2.40.

Alpha Stock Is Currently Trading at $34