Ima Greedy, the CFO of Financial Saving Techniques has been granted options on 200,000 shares. The stock is currently trading at $22 a share and the options are at the money. The variance of the stock has been about .07 on an annual basis over the last several years. The options mature in 3 years and the risk free rate is 4%.
-What is the value of a call option?
A)$4.14
B)$4.86
C)$5.13
D)$5.62
E)$6.16

Question

Quizplus · Accepted Answer

Using the Black-Scholes model, the value of the call option can be calculated as:

C = S*N(d1) – X*e^(-r*t)*N(d2)

Where:
S = stock price = $22
X = exercise price = $22
r = risk-free rate = 4%
t = time to maturity = 3 years
N() = standard normal cumulative distribution function
d1 = [ln(S/X) + (r + σ^2/2)*t] / [σ*sqrt(t)]
d2 = d1 – σ*sqrt(t)

σ = sqrt(V) = sqrt(0.07) = 0.2646 (annualized volatility)

Plugging in the values, we get:

d1 = [ln(22/22) + (0.04 + 0.07/2)*3] / [0.2646*sqrt(3)] = 0.6622
d2 = 0.6622 – 0.2646*sqrt(3) = -0.0567
N(d1) = 0.7458
N(d2) = 0.4765

C = 22*0.7458 – 22*e^(-0.04*3)*0.4765 = $5.13

Therefore, the value of the call option is $5.13. The correct choice is C.

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