Question

You own a​ one-year call option to buy one acre of Los Angeles real estate. The exercise price is​ $2.19 million, and the​ current, appraised market value of the land is​ $1.89 million. The land is currently used as a parking​ lot, generating just enough money to cover real estate taxes. The annual standard deviation is​ 16% and the interest rate​ 10%. How much is your call​ worth? Use the​ Black–Scholes formula

​(Answer in​ $000s with one decimal​ place.)

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		1890000
t = time to expiry =		1
K = Strike price =		2190000
r = Risk free rate =		10.0%
q = Dividend Yield =		0%
σ = Std dev =		16%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(1890000/2190000)+(0.1-0+0.16^2/2)*1)/(0.16*1^(1/2))
d1 = -0.215779
d2 = d1-σ*t^(1/2)
d2 =-0.215779-0.16*1^(1/2)
d2 = -0.375779
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.41458
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.353541
Value of call= 1890000*0.41458-0.353541*2190000*e^(-0.1*1)
Value of call= 82981.49 = 83 (000s)