Question

You own a lot in Bozeman, Montana that is currently unused. Similar lots have recently sold for $1.7 million. Over the past five years, the price of land in the area has increased 15 percent per year, with an annual standard deviation of 17 percent. A buyer has recently approached you and wants an option to buy the land in the next 10 months for $1,820,000. The risk-free rate of interest is 6 percent per year, compounded continuously.

How much should you charge for the option?

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =	1700000
t = time to expiry =	0.83333
K = Strike price =	1820000
r = Risk free rate =	6.0%
q = Dividend Yield =	0%
σ = Std dev =	17%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(1700000/1820000)+(0.06-0+0.17^2/2)*0.83333)/(0.17*0.83333^(1/2))
d1 = -0.039738
d2 = d1-σ*t^(1/2)
d2 =-0.039738-0.17*0.83333^(1/2)
d2 = -0.194926
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.484151
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.422726
Value of call= 1700000*0.484151-0.422726*1820000*e^(-0.06*0.83333)
Value of call= 91217.43