You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,270,000. Over the past five years, the price of land in the area has increased 7 percent per year, with an annual standard deviation of 36 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,420,000. The risk-free rate of interest is 5 percent per year, compounded continuously.
How much should you charge for the option?