Question

Use Black-Scholes to find the price for a put with 3 months to maturity. The exercise price is $75. The risk-free interest rate is 2.75% with continuous compounding. The stock price is $72. The historic VARIANCE is 0.0256. NOTE: Use the Black-Scholes template for this problem.

Answer 1

S = Current Stock Price =	$72
t = time until option maturity (years) = 3/12 =	0.25 years
K = Option Strike Price =	$75
r = risk free rate(annual) =	0.0275
s = standard deviation(annual) = sqrt(variance) = sqrt(0.0256) =	0.16
N = cumulative standard normal distribution
d1	= {ln (S/K) + (r +s^2/2)t}/s√t
	= {ln (72/75) + (0.0275 + 0.16^2/2)*0.25}/0.16*√0.25
	= -0.384300
d2	= d1 - s√t
	= -0.3843 - 0.16√0.25
	= -0.4643
Using z tables,
N(d1) =	0.3504
N(d2) =	0.3212
C = Call Premium =	=SN(d1) - N(d2)Ke^(-rt)
	= 72*0.3504 - 0.3212*75e^(-0.0275*0.25)
	= 1.3039
N(-d1) =	0.6496
N(-d2) =	0.6788
P = Put Premium =	=N(-d2)Ke^(-rt) - SN(-d1)
	= 0.6788*75e^(-0.0275*0.25) - 72*0.6496
	= 3.79

Hence, value of Put option = $3.79