SAN FRANCISCO -- If California energy officials had paid closer attention to mathematics and the commodities market yesterday, much of the state could be experiencing less of an energy crisis today. A systematic use of market contracts, called options, purchased before the crisis happened, might have alleviated it, says Philip Protter, a researcher at Cornell University in Ithaca, N.Y.

Protter stresses that it is unclear why new types of options, called energy derivatives, were not used to good effect. This, he says, could have been the fault of regulators, or utilities themselves, "or the inadequacies of what is, after all, a new kind of market."

Commodity options -- for electricity -- would have given California utilities the right to purchase excess capacity in the future at an agreed-upon price, says Protter, who is professor of operations research at Cornell. "They could have used options as a type of long-term insurance against the very events that transpired, provided, of course, they could have found sellers of those options. Energy market derivatives is a new field," he says.

That, says Protter in a talk prepared for the annual meeting of the American Association for the Advancement of Science, is what options are best used for: "A type of insurance against unlikely but potentially harmful financial events…it is a new kind of insurance without actuarial tables. But it is insurance, nevertheless."

Protter will present a talk on "Modeling Financially Risky Assets with Mathematics: A Little History and Some Explanations" at the San Francisco Hilton Hotel today

(Feb. 19, 11 a.m.). Like hog bellies and orange juice, electricity, natural gas and other forms of energy are all commodities. Buyers of commodities deal in forward contracts, future contracts or option contracts, hoping to hedge against possible price increases or decreases. These contracts can help the social good, Protter notes, by -- for example -- encouraging farmers not to slaughter livestock prematurely in order to profit from a later higher price; instead they can effectively lock in the higher price with a derivatives contract, such as a put option. In the same way, he says, utilities can be encouraged to lock in prices for electricity prices by buying contracts from suppliers ahead of their actual needs.

Although, he says, current mathematical models for describing the behavior of stocks or commodities are far from perfect, they are still capable of deducing trends. "This is the basis for informed long-term investing, as opposed to short-term speculation," Protter says. "The role of mathematicians arises in the analysis of financial derivatives, such as options. Here we, the mathematicians, supply the analysis that calculates fair prices and hedging strategies."

Indeed, he says, advanced mathematics has changed the way financial commerce is taking place today. "Higher mathematics has long had a place in explaining physics, chemistry, biology and engineering. What is new during the last 30 years is that it has changed modern commerce through the use of new and sophisticated financial tools, whose use mathematics has made possible. The advent of the systematic use of such tools as options has freed the market in ways analogous to the introduction of paper money millennia ago, or the introduction of credit, or more recently the introduction of wire transfers of money."

The primary use for these math-derived tools? Pricing and hedging of financial derivatives, used in the commodities markets, foreign exchange markets, in interest rates and in the stock market. "These mathematical models are used to let industry lay off risk," Protter says.

The contribution of mathematics to these transactions, Protter says, lies in a rational calculation of both the fair price for an option and the calculation of a hedging trading strategy to protect the seller of the option. This advance has led to today's ubiquity of options, from traded options listed on exchanges, to exotic and "boutique" options created by the banking industry.

"Just as it is hard to imaging life without the telephone, it has become hard to imagine modern commerce without financial derivative tools used to lay off risk," Protter says.