Markets can remain irrational longer than you can remain solvent.

—John Maynard Keynes

By the time Derman came to Goldman, Sachs in 1985, the use of the Black-Scholes equation to evaluate options had become commonplace. However, the equation had gotten off to a somewhat rocky start. In 1968, Scholes became an Assistant Professor of Finance at MIT in the Sloan School of Management. Black was a consultant for the Arthur D. Little Company in Cambridge. The two of them began collaborating on various economics problems. But at MIT there was also Paul Samuelson, one of the creators of modern mathematical economics. Samuelson had studied the use of Brownian motion to predict stock prices and two of his students, Richard Kruizinga and A. James Boness, had written theses attempting to use the model to derive values for options. Indeed, Kruizenga had cited Bachelier's work, so it was familiar at least at MIT. But it was left to Black and Scholes to finish the job. They first derived their...


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