Pricing the Future: Finance, Physics, and the 300-Year Journey to the Black-Scholes Equation by George Szpiro. Basic Books. $28. 320 pages.


Raleigh News & Observer & The Charlotte Observer

December 25, 2011

Math meets the markets in derivatives trading

BY PHILLIP MANning
 
Dozens of books with titles such as "Meltdown," "Busted," and Scott Patterson's "The Quants" have chronicled the financial debacle of 2008. ("Quants" are money managers who use computer-driven, quantitative trading strategies.) Patterson's book describes a Sept. 18 meeting between Federal Reserve chairman Ben Bernanke and several U.S. senators. The credit markets were frozen, Bernanke said. "We could have a depression if we don't act quickly and decisively."

Many investors believe the crisis was precipitated by the highly leveraged, rapid-fire trading of Ph.D. quants working in banks and hedge funds. In "Pricing the Future," George Szpiro recounts the history of quantitative investing. The well-told story reveals how quants came to dominate financial markets, and explains why they may endanger your 401K.

The tale centers on derivatives, contracts that give the purchaser the right to buy or sell something at a given price for a given period. Common derivatives such as stock options are not new. Futures contracts were being traded in Paris 200 years ago. Back then, options trading was wildly speculative because nobody could figure out the relationship between the price of a stock and its option.

The first step toward solving that mystery was taken by French mathematician Louis Bachelier. In 1900, Bachelier derived an equation that showed the value of an option depended on how much and how often the price of the underlying security changed and the time remaining on the option.

Over the years, mathematicians tried to improve on Bachelier's ideas. But progress was slow until 1969 when Fischer Black and Myron Scholes, two Ph.D. math whizzes, derived and solved a formidable differential equation. Szpiro sums up their accomplishment: "Black and Scholes had found the pricing formula for options."

The two published their discovery in 1973, and generously acknowledged another Ph.D., Robert Merton, who approached the problem differently but produced the identical equation.
"It would become," Szpiro says, "one of the most important papers ever in economics."

The equation is important because it gave quants a tool to establish arbitrage positions. (Arbitrage is the act of taking advantage of small price discrepancies between related assets.) Many hedge funds use one or more quantitative arbitrage methods, which now include derivatives far more complex than stock options. Despite, or maybe because of their sophisticated trading techniques, these funds have the power to rock financial markets.

A hedge fund named Long Term Capital Management provided an early example. Created in 1993, LTCM employed various quantitative arbitrage strategies. Because profit margins on arbitrage transactions are tiny, the partnership was highly leveraged. That is, it invested billions of dollars of borrowed money. At first, it grew rapidly. Then, a huge arbitrage position went south when Russia defaulted on its bonds. In a single day, the fund lost $551 million. That got the attention of the Federal Reserve, which decided that LTCM was "too big to fail." The Fed engineered a bailout, and the distressed firm was liquidated with huge losses for its investors.
LTCM's rescue set the stage for the 2008 "too big to fail" bailout by the Fed.

The discovery of the Black-Scholes equation, Szpiro says, "provided an intellectual milestone" that stimulated the growth of derivatives trading. But one should not blame it for today's financial problems. "This," he concludes, "would be like accusing Isaac Newton and the laws of motion for fatal traffic accidents."
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