You own a lot in Key West, Florida, that is currently unused. Similar lots have

Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,260,000. Over the past five years, the price of land in the area has increased 8 percent per year, with an annual standard deviation of 37 percent. You have approached a buyer and would like the option to sell the land in 12 months for $1,410,000. The risk-free rate of interest is 4 percent per year, compounded continuously.

What is the price of the put option necessary to guarantee your sales price?

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,260,000. Over the past five years, the price of land in the area has increased 8 percent per year, with an annual standard deviation of 37 percent. You have approached a buyer and would like the option to sell the land in 12 months for $1,410,000. The risk-free rate of interest is 4 percent per year, compounded continuously.

Explanation / Answer

Black-Scholes formula:

Put Option:

P = Xe-rt * N(-d2) – S0 e-rt * N(-d1)

The formulas for d1 and d2 are:

S0 = underlying price => $1,260,000

X = strike price => $1,410,000

= volatility = 37%

r = 8%

q = continuously compounded dividend yield => 0
t = time to expiration (% of year) => 100%

d1 = {ln($1,260,000/$1,410,000) + 1[(0.08 – 0)+(0.1369/2)}/ 0.37*(11/2) = 0.26919306
d2 = 0.269193061* (0.37*11/2)= 0.099601432

P = $1,410,000e-(008*1) * N(-0.099601432) + $1,260,000e-(0.08*1) * N(-0.26919306)
P = $209,496.286

So, value of the put option is $209,496.286

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