### Tip of the Week #58
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*Real Options: Managing Strategic Investment in an Uncertain World*

## by Martha Amram and Nalin Kulatilaka, 1999, Harvard Business School Press, 246 p.,
hardcover.

Options is one of the key topics in finance during the past three decades.
In 1969, Fischer Black, Robert Merton and Myron Scholes developed a new approach to
valuing options. This won Merton and Scholes the 1997 Nobel Prize in Economics.
The Black-Scholes equation for pricing European options became the genesis of a
whole industry in derivatives markets.

The classic option problem is this: What is the value of a call option (a right to
buy an asset) for a stock, at some future date, for a stated amount? The inputs to
the Black-Scholes equation are:

- Current value of the asset
- Time to the decision date
- The asset's annual price volatility
- The investment amount (exercise price)
- The risk free rate of return [This catches my attention! Perhaps
this supports using a (nearly) risk-free NPV discount rate.]

There are various adjustments for different structures (especially American
options where the option can be exercised at any time before expiration) and for
convenience yields. Solution methods include partial differential equations, dynamic
programming, and Monte Carlo simulation. The book includes example calculations with
the Black-Scholes analytic solution and the binomial tree as a dynamic programming
solution.

Decision analysts have been solving option
problems for decades with decision trees, where every subsequent decision node represents
an option. |

Periodic papers have been appearing in the petroleum industry for some years about
valuing options to drill and develop. The calculations are not difficult, though one
must accept the premises, such as a lognormal process. It remains to be seen whether
a real options approach will become popular. I'm hopeful that we might be able to
derive a consensus oil price forecast from futures markets. [If you have seen this
done somewhere, please email .] Also, I think the real options approach would be
useful for reasonableness tests.

This book is long on selling the approach and short on the details. There is
some additional information at the authors' Web site: http://www.real-options.com. I recommend this
book for what I got from it: a tutorial about options. If you want to actually do
these calculations, then you'll want to seek additional details in the referenced books
and papers.

—John Schuyler, July 1999

Copyright © 1999 by John R. Schuyler. All rights reserved. Permission to copy with
reproduction of this notice.