Question

You own a lot in Montreal that is currently unused. Similar lots have recently sold for $1.9 million. Over the past five years, the price of land in the area has increased 12 percent per year, with an annual standard deviation of 25 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $2.1 million. The risk-free rate of interest is 5 percent per year, compounded continuously.

How much should you charge for the option? Suppose you wanted the option to sell the land to the buyer in one year. What is the price of the transaction today?

Answer 1

The option to buy the lot is a call option and the option to sell the lot is a put option. Using Black-Scholes model, we have:

Inputs: Current stock price (S) Strike price (K) Time until expiration in years) volatility (s) risk-free rate (0) 1.90 2.10 1.000 25.0% 5.00% Formulae: d1 = {In(S/K) + (r +s^2/2)t(s(t^0.5) d2 = d1 - (s(t^0.5)) Nd1) - Normal distribution of d1 N(-d1) - Normal distribution of -d1 N(D2) - Normal distribution of d2 IN(-d2) - Normal distribution of -d2 C = S*N(1) - N(d2)*K*e^(-1t)) P = K (^-rt) *N(-d2) - SN(-d1)

Output: Ble. N(d1) N(-d1) N(02) N(-d2) Call premium (C) Put premium (P) (0.0753) (0.3253) 0.4700 0.5300 0.3725 0.6275 0.1489 0.2465

The option to buy the lot one year hence, is worth $0.1489 million. The option to sell the lot one year hence, is worth $0.2465 million.