Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,330,000. Over the past five years, the price of land in the area has increased 7 percent per year, with an annual standard deviation of 33 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,480,000. The risk-free rate of interest is 3 percent per year, compounded continuously. How much should you charge for the option? Call price $

Answer 1

It can be calculated using the Black Scholes model.

Risk free rate = 3%

Standard Deviation = 33%

Spot rate = $ 1,330,000

Strike price = $ 1,480,000

putting above values,

d1 = (ln(1,330,000/1,480,000) + (0.03+ 0.33^2/2)*1)/0.33*sqrt(1) = -0.0679

d2 = d1 - 0.33*sqrt(1) = -0.3979

Value of call = 1,330,000*N(d1) - N(d2)*1,480,000*exp(-0.03*1) = $ 132985.403