Question

4.  Problem 18.04 (Black-Scholes Model)

Assume that you have been given the following information on Purcell Industries:

Current stock price = $16
Exercise price of option = $16
Time until expiration of option = 6 months
Risk-free rate = 11%
Variance of stock price = 0.07
= 0.38753
= 0.20045
= 0.65082
= 0.57943

Using the Black-Scholes Option Pricing Model, what is the value of the option? Round intermediate calculations to 4 decimal places. Round you answer to the nearest cent.

$  

Answer 1

std dev = var^(1/2) = 0.07^(1/2) = 26.45%

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		16
t = time to expiry =		0.5
K = Strike price =		16
r = Risk free rate =		11.0%
q = Dividend Yield =		0%
σ = Std dev =		26%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(16/16)+(0.11-0+0.2645^2/2)*0.5)/(0.2645*0.5^(1/2))
d1 = 0.387586
d2 = d1-σ*t^(1/2)
d2 =0.387586-0.2645*0.5^(1/2)
d2 = 0.200556
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.650839
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.579477
Value of call= 16*0.650839-0.579477*16*e^(-0.11*0.5)
Value of call= 1.64