--Nathan Newman =========
August 16, 1999
PATENTS Calculating the Value of Derivatives By TERESA RIORDAN
lan Greenspan, the chairman of the Federal Reserve Board, estimated earlier this year that the financial derivatives market was worth some $80 trillion.
But exactly how do you go about calculating the worth of financial derivatives -- securities whose value is derived from an underlying asset, like a stock, bond or currency? If Goldman, Sachs is thinking about buying a basket of 30-year mortgages, for example, how can it grasp the slippery value of such a complicated asset?
One way is to use a statistical technique known as Monte Carlo, which was devised in the late 1940s by hydrogen-bomb designers at Los Alamos, N.M., who realized they could not solve nuclear-fusion equations by conventional means. Monte Carlo is a broad idea that has since been applied in many different ways in many different fields, from physics to finance.
In 1992, Irwin Vanderhoof, a professor of finance at New York University, suspected that another technique -- sometimes referred to as quasi-Monte Carlo -- might give speedier, more accurate results when the value of financial derivatives and other complex securities is calculated.
It was a suspicion that was not shared by others. "Nobody believed in the early '90s that this could be superior to Monte Carlo," said Joseph Traub, a professor of computer science at Columbia University.
Vanderhoof arranged for Goldman, Sachs to give Traub a difficult problem -- figuring the value of a collateralized mortgage obligation, which is essentially a collection of 30-year mortgages whose worth is difficult to fix because of varying interest rates and unpredictable prepayments.
Spassimir Paskov, then one of Traub's graduate students, valued the mortgages using both Monte Carlo and quasi-Monte Carlo.
"To our amazement, we found that quasi-Monte Carlo consistently beat Monte Carlo by a factor of 10 to 1,000," Traub said.
On Tuesday, Traub, Vanderhoof and Paskov will receive a patent for their use of this numerical technique for assessing the value of complex securities like derivatives.
So what is the difference between regular Monte Carlo and quasi-Monte Carlo? To understand, imagine trying to estimate the average depth of a pond.
With Monte Carlo, one would take measurements of the pond's depth at random points. If the points are plotted on an aerial drawing of the pond, some areas will be pocked with points while other areas will be bare.
With quasi-Monte Carlo, depth measurements are taken at points that have been selected deterministically -- that is, with a formula. If the points are plotted on an aerial picture of the pond, they will be scattered in an even, patterned fashion, with no bare spots or clusters.
"In quasi-Monte Carlo, the points are chosen uniformly with as few points as possible such that the average of the measured depth is close to the true average depth," Traub said.
Why does quasi-Monte Carlo work faster and more accurately than the regular Monte Carlo? It could have to do with the fact that when cash flows are figured, near-term variables carry much more weight than variables in the distant future. "Clearly there is something special about finance problems," Traub said.
Paskov, who is now an associate director in risk management for the investment arm of Barclays Bank, built a software system that uses the quasi-Monte Carlo to value derivatives and other complex securities. The software, called Finder, is being licensed by Columbia University to investment houses and insurance companies.
Traub, Vanderhoof and Paskov will receive patent 5,940,810.