A Man for All Markets by Edward O. Thorp

Author:Edward O. Thorp
Language: eng
Format: epub
Publisher: Random House Publishing Group
Published: 2017-01-24T05:00:00+00:00

Chapter 14

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FRONT-RUNNING THE QUANTITATIVE REVOLUTION

When Black and Scholes published their formula, the same one I was already using, I knew that to maintain PNP’s trading edge I would have to develop my tools for valuing warrants, options, convertible bonds, and other derivative securities rapidly enough to stay ahead of future marching legions of PhDs hungry for academic advancement through publication. Though I had to keep important results secret for the benefit of our investors, I could publicize lesser ideas that I thought would soon be found by others.

Before the work of Black and Scholes, I had moved beyond their basic formula, having generalized it to include cases where short-sale proceeds were withheld by the broker (to his benefit, since he got the use of the money) until the short sale was closed. Once they published, I presented these at a meeting of the International Statistical Institute in Vienna, where I was speaking. I also had extended the model to include dividend-paying stocks, since I was trading call options and warrants on many such stocks. Then the CBOE announced it would start trading put options sometime in the following year, 1974. These options, like the call options we were already trading, were called American options, as distinguished from European options. European options can be exercised only during a short settlement period just prior to expiration, whereas American options can be exercised anytime during their life.

If the underlying stock pays no dividends, the Black-Scholes formula, which is for the European call option, turns out to coincide with the formula for the American call option, which is the type that trades on the CBOE. A formula for the European put option can be obtained using the formula for the European call option. But the math for American put options differs from that for European put options, and—even now—no general formula has ever been found. I realized that I could use a computer and my undisclosed “integral method” for valuing options to get numerical results to any desired degree of accuracy for this as-yet-unsolved “American put problem.” In a productive hour in the fall of 1973 I outlined the solution, from which my staff programmed a computer to produce precise calculated values. My integral method also had another advantage over the Black-Scholes approach. Whereas the latter was based on one specific model for stock prices, one with limited accuracy, my technique could value options for a wide range of assumed distributions of stock prices.

In May 1974 I had dinner with Fischer Black in Chicago, where he had invited me to give a talk at the semiannual CRSP (Center for Research in Security Prices) meeting at the University of Chicago. Then in his thirties, Fischer was trim and tall, with combed-back black hair and “serious” glasses. Focusing intently on whatever finance topic was being discussed, he spoke articulately, logically, and concisely. His notes, compact and ultra-legible, reflected this. He would go on to become one of the most innovative and influential figures in academic and applied finance.

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