Andrew Allentuck

Monday, November 5, 2001

Option Pricing - Black-Scholes Made Easy: A Visual Way to Understand Stock Options, Option Prices, and Stock Market Volatility
by Jerry Marlow
John Wiley & Sons, 2001
333 pages, CD-ROM
ISBN 0-471-43641-0

Freelance financial writer Jerry Marlow has rendered a major service in mapping the results of using the Black-Scholes option pricing formula. The partial differential equation they created made it possible to set a price on a thing of value under conditions of uncertainty. Their work has roots that go back to a French mathematician who cerebrated on stock prices on the Paris bourse a century ago and to Einstein's work on the random motion of particles. Now installed in many handheld personal digital assistants, the formula turned options from a cult for commodities cognoscenti into a major market with trillions in annual trades.

Understanding Black-Scholes' partial differential equation is not really so hard, but seeing the results really is tough to do. Marlow's contribution is in running simulations and printing his computer screen's results. Along with instructions on how to run the same simulations, he offers an understanding of how options price forecasts can move toward exchange prices that clear transactions.

A cottage industry has developed around the Black-Scholes model. By varying assumptions, traders and academics have dealt with such problems in the model as lack of normally distributed returns, market illiquidity, and the wobbliness of prices over time and certain properties of nonconformity to assumed price functions. What all that means is that attempts to connect the dots may produce incorrect equilibrium prices for options, as Marlow makes clear.

So crunch with care. Careful use of this book will enhance understanding of the Black-Scholes formula and show why they and Robert Merton won the Nobel Prize in 1997. If you want to see the formula at work, then get this book. Other books explain the equation and some do it in simpler terms. This is the formula without all the math. Marlow has made a valuable contribution to the understanding of contemporary, mathematical finance.