Question

Calculate the price of a European call option using the Black Scholes model and the following data: stock price = $56.80, exercise price = $55, time to expiration = 15 days, risk-free rate = 2.5%, standard deviation = 22%, dividend yield = 8%.

Answer 1

As per Black Scholes Model
Value of call option = S*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		56.8
t = time to expiry =		0.041666667
K = Strike price =		55
r = Risk free rate =		2.5%
q = Dividend Yield =		8%
σ = Std dev =		22%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(56.8/55)+(0.025-0.08+0.22^2/2)*0.0416666666666667)/(0.22*0.0416666666666667^(1/2))
d1 = 0.688525
d2 = d1-σ*t^(1/2)
d2 =0.688525-0.22*0.0416666666666667^(1/2)
d2 = 0.643618
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.754439
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.740088
Value of call= 56.8*0.754439-0.740088*55*e^(-0.025*0.0416666666666667)
Value of call= 2.19