Following is formula to calculate the value of call option under the Black-Scholes Model
Vc = P*N (d1) - N (d2) *X*e ^ (-r*t)
Where
Vc = call value
P = current stock price = $27
N = cumulative standard normal probability distribution
t = days until expiration = 6 months = 0.5 years
Standard deviation, SD = σ = 0.3317
X = option strike price = $25
r = risk free interest rate = 6%
e = exponential function = 2.7183
Formula to calculate d1 and d2 are -
d1 = {ln (P/X) +(r+ σ^2 /2)* t}/σ *√t
= {ln(27/25) + (6%+0.11/2)*0.5}/0.3317 *√0.5
=0.5733
d2 = d1 – σ *√t
= 0.5733 – 0.3317*√0.5 = 0.3388
Now putting the value of d1 and d2 in above equation
Vc = $27*N (0.5733) - N (0.3388) *$25*2.7183 ^ (-6%*0.5)
= $4.0054
Call value (Vc) is $4.0054
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