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# Option on land

Discussion in 'Options' started by 9999, May 13, 2007.

1. ### 9999

Hey guys,
I need to calculate the value of an option on a piece of land.

2. ### nonprophet

IMO Black-Scholes will do just fine here, but you'll need to input some volatility.

Or, here's a text I copied a while ago:

You would like to buy a 1-year call option on a piece of land. Unfortunately, the landowner is unwilling to sell you a call option but is willing to sell the land for \$1,000,000. Assume that the 1-year risk-free rate of interest is 10%, that you could borrow as much as \$900,000 to purchase the land if you also buy an insurance policy which will pay off the loan if you do not pay the loanâs par value. The cost of the insurance is \$5,000.

Even though the landowner will not sell you a call option directly, you can replicate the outcomes of a call on the land by taking the following steps. First, buy the insurance policy for \$5,000 and arrange a 1-year loan with a par value of \$900,000. Based on a 10% interest rate and a 1-year repayment, you will be able to borrow \$818,182 (\$900,000 Ã· 1.1). Thus, your personal down payment on the land will have to be \$181,818. Adding in the insurance cost, the total cost to you will be \$186,818.

When the loan is to be repaid in 1-year, you will repay it if the land is worth more than the required \$900,000 loan payment. If the land is worth less than \$900,000, you will default on the loan and let the insurance policy pay the lender any difference between the landâs value and the required loan payment. The outcome is identical to owning a 1-year call option on the land with an exercise price of \$900,000! And the cost of this replicated call option is \$186,812:

Replicated Call = Buy Spot Asset - Debt Financing + Insurance Cost

+C = +S - [X Ã· (1+RF)^T] + P

\$186,812 = \$1,000,000 - [\$900,000 Ã· 1.11] + \$5,000

3. ### Batman28

This has nothing to do with Black-Scholes, and volatility input is not required.

What you're refering to is known as a "real option". google it, buy books on it or take an MBA (they all cover it these days). it's one of the newest growing areas in finance & management.

the copied text above from nonprophet is also an example of a real option.

4. ### kinggyppo

there are many variables, assuming this is not a hypothetical case. What are the terms, ie date, price, concessions, etc. you are in the wrong area maybe. May want to be on a real estate forum.

5. ### 9999

Thank you guys.
Any good real estate forum?

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