Columbia University New York, N.Y. 10027 Office of Public Information (212) 854-5573
Computer scientists at Columbia University have developed a technique that will allow market traders to set prices for complex financial instruments more quickly, accurately and with greater confidence than the standard now in use.
The technique, embodied in software created at the University, can solve highly complex problems that involve as many as 360 variables. Called deterministic low-discrepancy sampling, it is described for the first time by Joseph Traub, the Edwin Howard Armstrong Professor of Computer Science at Columbia, and Spassimir Paskov, a Columbia Ph.D., in the fall issue of the Journal of Portfolio Management. Issues of the journal are being mailed this week.
The software, named FINDER for "financial derivatives," can be used to more rapidly determine the value of derivatives, which include options, futures and mortgage-backed securities. Software licenses for FINDER are available through Columbia Innovation Enterprise, the University's technology transfer and licensing organization.
Faster and more accurate pricing for derivatives would boost a trading firm's confidence in the prices it sets, permitting it to sell the complex instruments with lower risk. The value of a derivative is based on its assets -- stocks, bonds or loans with periodic interest or dividend payments. For example, in pricing a mortgage-backed security, a trader must consider each monthly payment a separate variable. A derivative based on a basket of 30-year mortgages requires analysis of 360 variables.
Such problems suffer from what mathematicians call the "curse of dimensionality," in which complexity increases exponentially with the number of variables. Even with fast computers, a solution used to take weeks.
Wall Street has long used the Monte Carlo method, which averages the values of a random sample of points, to speed the computation. The Columbia researchers instead chose another method of sampling points, one far more likely to deliver a correct answer, the deterministic low-discrepancy approach.
The Columbia researchers applied the technique to a difficult problem supplied to them by Goldman Sachs, the New York investment house: valuing a 30-year mortgage-backed security divided into 10 shares, or tranches. Because the Goldman Sachs model permitted monthly changes in interest rates and prepayment percentages, the problem to be solved has 360 dimensions.
Professor Traub and his graduate student expected that low-discrepancy methods and the Monte Carlo technique would prove equally adept at solving the problem, but found to their amazement that low-discrepancy consistently beat Monte Carlo for accuracy, confidence and speed.
The Columbia team first became interested in the approach after Henryk Wozniakowski, professor of computer science at Columbia, in 1991 published a solution to a 20-year-old problem on optimal choices of sample points in the Bulletin of the American Mathematical Society.
A software product based on the deterministic low-discrepancy approach was recently announced by IBM. At a Sept. 27 press conference in New York, the company described its Deterministic Simulation Blaster, which IBM said would allow securities firms to refine their mathematical projections of derivatives' values and determine a price that would put traders at lower risk.
The Columbia computer scientists pioneered the application of deterministic sampling to the pricing of financial derivatives. The Journal of Portfolio Management article is the first published research on the subject.
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