Vol.25, No. 01	Sept. 3, 1999

CU Receives Patent for Traub’s Fast Method to Value Complex Securities

By Bob Nelson

Columbia University now holds the patent for the work of three New York inventors who have shown that complex securities can be valued much faster and more accurately than by the method widely used by financial institutions.

Joseph F. Traub, the Edwin Howard Armstrong Professor of Computer Science at Columbia; Spassimir Paskov, a former Ph.D. student of Professor Traub's, now associate director in risk management at the New York office of Barclays Capital, the investment arm of Barclays Bank; and Irwin Vanderhoof, professor of finance at NYU, have received a patent issued on Aug. 17 (Patent # 5,940,810). The patent has been assigned to Columbia University, where the work was conducted.

A very important instance of a complex security is a financial derivative, that is, an instrument whose value is derived from an underlying asset. The significance of this innovation is illustrated by the size of the derivatives market which, according to Alan Greenspan, the chairman of the Federal Reserve, had an estimated value of $70 trillion in 1998 and as much as $80 trillion in 1999 (New York Times, March 20, 1999).

Financial derivatives can be extremely complicated and require large amounts of computer time to value. An example of a financial derivative is a collateralized mortgage obligation (CMO), which is constructed from a mortgage pool. Assuming that the pool consists of 30-year mortgages and that the interest rate and prepayments can change monthly, the expected cash flows from the pool is a problem that must be solved in 360 variables.

The usual method employed by financial institutions to value financial derivatives is called Monte Carlo. To understand the idea behind Monte Carlo, consider the problem of estimating the average depth of a pond with an uneven bottom. Points at which the depth is measured are chosen at random. The average depth is estimated by the average of the measurement depths.

In quasi-Monte Carlo, the points are chosen uniformly with as few points as possible such that the average of the measured depths is close to the true average depth. These are known as low discrepancy points and are given by a formula rather than chosen at random. This is a problem in two variables, the coordinates of the pond's surface, while the CMO problem is in 360 variables. Measuring the "depths" in the CMO problem is extremely expensive; it can take a million computer operations to value a single complex security by sampling points. It is therefore advantageous to choose as few points as possible.

The conventional wisdom in the early 1990s, shared by the world's leading experts, was that quasi-Monte Carlo would not be effective for problems with more than a dozen or so variables.

In 1992, Vanderhoof saw comment in a technical publication on the work of Henryk Wozniakowski, professor of computer science at Columbia, and realized that Wozniakowski's results on quasi-Monte Carlo could be applied to complex securities. He arranged to have the New York investment house, Goldman Sachs and Co., give a complicated CMO to Traub, who asked one of his Ph.D. students, Paskov, to try valuing this CMO using both Monte Carlo and quasi-Monte Carlo methods.

To their amazement, quasi-Monte Carlo was faster than Monte Carlo by factors ranging from ten to a thousand. It was also more accurate.

Paskov built a software system called FINDER (FINancial DERivatives) that uses quasi-Monte Carlo to value financial derivatives and other complex securities. He made major improvements in known quasi-Monte Carlo methods and incorporated them into FINDER. After Paskov received his Ph.D. and left Columbia, Anargyros Papageorgiou, a former Ph.D. student of Traub's and now a research scientist at Columbia, made further improvements to FINDER. FINDER is available on various platforms, including Windows 95/NT and UNIX. It integrates easily with custom and off-the-shelf applications. A version of FINDER is available as a Microsoft Excel add-in. To learn more about FINDER and to see the results of using quasi-Monte Carlo and Monte Carlo on a variety of instruments, go to http://www.cs.columbia.edu/~traub.