Question

. Assume the following for a stock and a call and a put option written on the stock.

EXERCISE PRICE = $20

CURRENT STOCK PRICE = $22

VARIANCE = .25

Standard Deviation = .50

TIME TO EXPIRATION = 4 MONTHS  T = .33

RISK FREE RATE = 3%

Use the Black Scholes procedure to determine the value of the call option and the value of a put.

Answer 1

S = Current Stock Price =	22
t = time until option expiration(years) =	0.3300
X = Option Strike Price =	20
r = risk free rate(annual) =	0.0300
s = standard deviation(annual) =	0.50
N = cumulative standard normal distribution
d1	= {ln (S/K) + (r +s^2/2)t}/s√t
	= {ln (22/20) + (0.03 + 0.5^2/2)*0.33}/0.5*√0.33
	0.509900
d2	= d1 - s√t
	= 0.5099 - 0.5√0.33
	0.2227
Using z tables,
N(d1) =	0.6949
N(d2) =	0.5881
C = Call Premium =	=SN(d1) - N(d2)Ke^(-rt)
	= 22*0.6949 - 0.5881*20e^(-0.03*0.33)
	3.6417
N(-d1) =	0.3051
N(-d2) =	0.4119
P = Put Premium =	=N(-d2)Ke^(-rt) - SN(-d1)
	= 0.4119*20e^(-0.03*0.33) - 22*0.3051
	1.4446

Hence, value of call option = $3.64 and value of put option = $1.44