Investment Theory and Risk Management, + Website

Real Options

Luenberger (1998) has a very nice running application throughout his book on the value of a lease to a gold mine. Conceptually, the decision to lease the mine depends on the perceived value of the lease relative to the asking price. Because the value of the lease depends on the price of gold, which is stochastic, then the lease itself is a derivative security. If gold's price dynamic is modeled using a lattice, then we can essentially determine the value of the lease, today, as the weighted present value of the complete set of state prices. This part of the problem is easy to solve because it follows directly from our earlier work on options. What makes the gold mine lease especially interesting is Luenberger's use of inherent optionality. In his example, the owner of the mine has the option at any time over the life of the lease of purchasing at fixed cost a production enhancement that improves the mine's output. Naturally, the likelihood of exercising this option will depend on the path that gold prices follow. The question we seek an answer to is how this option affects the value of the lease today.

Example 16.2

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Let's suppose it is December 30, 2001, and we are contemplating a 10-year lease on this mine. The price of gold on that date was $278 per ounce and the trailing annual volatility of gold prices from 1970 through ...