Question

What is the price of a $25 strike call? Assume S = $23.50, σ = 0.24, r = 0.055, the stock pays a 2.5% continuous dividend and the option expires in 45 days? SHOW WORK PLS A) $0.60 B) $0.50 C) $0.40 D) $0.30

Answer 1

As per Black Scholes Model
Value of call option = S*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		23.5
t = time to expiry =		0.125
K = Strike price =		25
r = Risk free rate =		5.5%
q = Dividend Yield =		2.50%
σ = Std dev =		24%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(23.5/25)+(0.055-0.025+0.24^2/2)*0.125)/(0.24*0.125^(1/2))
d1 = -0.642588
d2 = d1-σ*t^(1/2)
d2 =-0.642588-0.24*0.125^(1/2)
d2 = -0.727441
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.260246
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.233478
Value of call= 23.5*0.260246-0.233478*25*e^(-0.055*0.125)
Value of call= 0.32