Question

Ignore transaction costs and other imperfections for the problem

a. You own a piece of land in a prime location that is currently unused. Similar lots have recently sold for $3 million. Over the past five years, the price of land in the area has increased by 10 percent per year, with an annual standard deviation of 20 percent. A potential buyer has recently approached you and wants an option to buy the land in the next 6 months for $3.2 million. The risk-free rate of interest is 5 percent per year, compounded continuously. Use the Black-Scholes option pricing model to determine how much you should charge for the option.

b. Suppose instead that you wanted the option to sell the land to the potential buyer in 6 months. Assuming all the facts are the same, what should be the price of the option today?

Answer #1

The Black Scholes formula is written as:

or

Where,

C = Option price

S is the underlying price of the land = 3 million

X is the exercise price of the land = $3.2 million

t is the length of time for the decision to be made to exercise the option = 6 months

r is the risk free rate of return = 5%

= standard deviation = 20%

Ans. a. By solving the above equations, we get the Option price (C) = $ 118,717

Ans. b. By solving the above equations, we get the Put price (P) = $ 239,709

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