Question

Question #1: Use the Black-Scholes formula to find the value of a call option on the following stock: 6 months 50% per year Time to expiration Standard Deviation Exercise Price Stock Price Interest Rate $50 $50 10% Question #2: Find the value of put option on the stock in the previous problem with the same information above (Hint: there are two ways of calculating such value).

show how its done. thank you

Answer 1

1. Call Option

S = Current Stock Price =	50
t = time until option expiration(years) = 6/12 =	0.5000
X = Option Strike Price =	50
r = risk free rate(annual) = 10/100 =	0.10
s = standard deviation(annual) = 50/100 =	0.50
N = cumulative standard normal distribution
d1	= {ln (S/K) + (r +s^2/2)t}/s√t
	= {ln (50/50) + (0.1 + 0.5^2/2)*0.5}/0.5*√0.5
	= 0.3182
d2	= d1 - s√t
	= 0.3182 - 0.5√0.5
	= -0.0354
Using z tables,
N(d1) =	0.6248
N(d2) =	0.4859
C = Call Premium =	=SN(d1) - N(d2)Ke^(-rt)
	= 50*0.6248 - 0.4859*50e^(-0.1*0.5)
	= 8.1299

Value of Call option = $8.13

2. Put Option

S = Current Stock Price =	50
t = time until option expiration(years) = 6/12 =	0.5000
X = Option Strike Price =	50
r = risk free rate(annual) = 10/100 =	0.10
s = standard deviation(annual) = 50/100 =	0.50
N = cumulative standard normal distribution
d1	= {ln (S/K) + (r +s^2/2)t}/s√t
	= {ln (50/50) + (0.1 + 0.5^2/2)*0.5}/0.5*√0.5
	0.3182
d2	= d1 - s√t
	= 0.3182 - 0.5√0.5
	= -0.0354
Using z tables,
N(-d1) =	0.3752
N(-d2) =	0.5141
P = Put Premium =	=N(-d2)Ke^(-rt) - SN(-d1)
	= 0.5141*50e^(-0.1*0.5) - 50*0.3752
	= 5.6914

Value of Put option = $5.69