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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:
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.