Question

Assume that the current XYZ stock price is equal to $33, the volatility of XYZ is 32%, and XYZ stock pays 1% dividends each year. The risk free interest rate is 6% today. Consider an European call option with a strike price of $35, and suppose that the option will be expired after 68 days from today (1 year = 365 days). Then, what is the value of the call option?

Answer 1

As per Black Scholes Model
Value of call option = S*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		33
t = time to expiry =		0.18630137
K = Strike price =		35
r = Risk free rate =		6.0%
q = Dividend Yield =		1.0%
σ = Std dev =		32%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(33/35)+(0.06-0.01+0.32^2/2)*0.186301369863014)/(0.32*0.186301369863014^(1/2))
d1 = -0.289507
d2 = d1-σ*t^(1/2)
d2 =-0.289507-0.32*0.186301369863014^(1/2)
d2 = -0.427627
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.386097
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.334461
Value of call= 33*0.386097-0.334461*35*e^(-0.06*0.186301369863014)
Value of call= 1.17