Question

What is the price of a European call option according to the Black-Sholes formula on a non-dividend-paying stock when the stock price is $45, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 25% per annum, and the time to maturity is six months? Show your work in details.

Answer 1

S = Current Stock Price =	45
t = time until option expiration(years) = 6/12 =	0.5000
X = Option Strike Price =	50
r = risk free rate(annual) = 12/100 =	0.12
s = standard deviation(annual) = 25/100 =	0.25
N = cumulative standard normal distribution
d1	= {ln (S/K) + (r +s^2/2)t}/s√t
	= {ln (45/50) + (0.12 + 0.25^2/2)*0.5}/0.25*√0.5
	= -0.1682
d2	= d1 - s√t
	= -0.1682 - 0.25√0.5
	= -0.3450
Using z tables,
N(d1) =	0.4332
N(d2) =	0.3650
C = Call Premium =	=SN(d1) - N(d2)Ke^(-rt)
	= 45*0.4332 - 0.365*50e^(-0.12*0.5)
	= 2.3068

Hence, Value of call option = $2.31