Question

QUESTION 9 15 points Save Answer A European PUT option written on one share of Deadwood Lumber Co. stock has the following parameter values: S = $28, X = $30, r = 5% p.a., o = 20% p.a., T = 6 months. Find the premium of this option, rounded to 2 decimals (e.g., 1.15; do NOT include a dollar sign in your answer). NOTE: Use the continuous time version of the Black-Scholes and Put-Call Parity equations (i.e., do NOT use the book's version). Help

Answer 1

Using Black Scholes model -

S = Current Stock Price =	28
t = time until option expiration(years) = 6/12 =	0.50
X = Option Strike Price =	30
r = risk free rate(annual) = 5/100 =	0.05
s = standard deviation(annual) = 20/100 =	0.2
N = cumulative standard normal distribution
d1	= {ln (S/K) + (r +s^2/2)t}/s√t
	= {ln (28/30) + (0.05 + 0.2^2/2)*0.5}/0.2*√0.5
	= -0.2404
d2	= d1 - s√t
	= -0.2404 - 0.2√0.5
	= -0.3818
Using z tables,
N(-d1) =	0.5950
N(-d2) =	0.6487
P = Put Premium =	=N(-d2)Ke^(-rt) - SN(-d1)
	= 0.6487*30e^(-0.05*0.5) - 28*0.595
	2.3205

Hence, Value of Put Option = $2.32