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 / Spring 2006 / Issue 42(originally published by Booz & Company)


Derivative Wisdom

In Fischer Black and the Revolutionary Idea of Finance, Perry Mehrling explains how Dr. Black’s training as a physicist equipped him to discover the key to the problem.

Lacking the ability to run controlled experiments on the stars, the astrophysicist relies on careful observation and then imagination to find the simplicity underlying apparent complexity. In Fischer’s hands, the same habits of research turned out to be effective for producing new knowledge in finance.

After considerable trial and error and with the aid of sophisticated mathematics, Dr. Black and Dr. Scholes created a model for valuing options that included five variables: the stock’s price at the time of valuation, the exercise price (the price at the time the option would be used), the time to maturity, and the interest rate on risk-free assets — all of which could be directly observed — plus a measure of the volatility of the underlying stock.

If the Black–Scholes formula had merely solved a problem applicable to an obscure class of financial instruments, it would rate a mere footnote in financial history. It turned out, however, to have vastly greater applications than even its creators imagined. The stock option, viewed through the lens of Black–Scholes, is a synthetic, or derivative, security. Unlike a stock or bond, which represents ownership in tangible assets, an option derives its value from the movements of the five factors that Dr. Black and Dr. Scholes identified. By identifying and quantifying the interrelationships among these factors, their formula made it possible to construct a new universe of derivatives, allowing banks, brokers, corporations, investors, money managers, and speculators to design and trade financial instruments tailored for exactly the kinds of risks they want to hedge against or profit from.

Black–Scholes appeared at a fortuitous time. As its creators were preparing to publish their formula in The Journal of Political Economy in 1973, the Chicago Board Options Exchange opened, creating an organized market for financial derivatives. Later that year, the Organization of Petroleum Exporting Countries (OPEC) raised the price of crude oil by 70 percent, helping initiate the greatest period of financial instability since the Great Depression. Technological advance also played a part: Calculating Black–Scholes prices by hand is a tedious process requiring precision and advanced math skills, and harnessing the mainframe computers in use in the 1970s was too cumbersome and slow for traders and analysts. But six months after the Black–Scholes formula was published, Texas Instruments introduced a handheld calculator programmed to do the math, announcing it with a half-page ad in the Wall Street Journal. Suddenly, any bright practitioner could instantly compute options prices that previously had been a mystery to everybody.

“It was as though, in a thirsty world filled with hydrogen and oxygen, someone had finally figured out how to synthesize H2O,” writes Emanuel Derman in My Life as a Quant. Dr. Derman goes on to say that “the history of quants on Wall Street is the history of the ways in which practitioners and academics have refined and extended the Black–Scholes model. The last thirty years have seen it applied not just to stock options but to options on just about anything you can think of, from Treasury bonds and foreign exchange to the weather.”

Physics for Financiers
Like Fischer Black, Emanuel Derman set out to become a physicist, but he stuck with it longer. My Life as a Quant: Reflections on Physics and Finance, his autobiography, is a highly readable account of the financial revolution on Wall Street, and the best single book that this writer has seen about modern finance. It enables those of us challenged by higher math to understand the intellectual elegance of the field, and also shows vividly the capitalistic hurly-burly that took place on Wall Street as the traders and markets absorbed the sudden blast of new ideas and found ways to harness them.

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Modern Finance Resources:
Works mentioned in this review.

  1. Peter L. Bernstein, Against the Gods: The Remarkable Story of Risk (John Wiley & Sons, 1996), 400 pages, $19.95
  2. Peter L. Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street (Free Press, 1992; John Wiley & Sons, 2005), 352 pages, $16.95
  3. Emanuel Derman, My Life as a Quant: Reflections on Physics and Finance (John Wiley & Sons, 2004), 304 pages, $29.95
  4. Perry Mehrling, Fischer Black and the Revolutionary Idea of Finance (John Wiley & Sons, 2005), 392 pages, $29.95
  5. Hersh Shefrin, Beyond Greed and Fear: Understanding Behavioral Finance and the Psychology of Investing (Harvard Business School Press, 2000), 378 pages, $44.50
  6. Lauren Aguirre et al., “Trillion Dollar Bet,” Web site based on the February 8, 2000, WGBH Nova documentary: Click here. 
  7. Wikipedia, the free online encyclopedia edited by its readers: Click here.
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