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Significant Flaws Uncovered in Standard Securities Derivatives Models

Many securities transactions do not involve the direct purchase of securities. Instead, they consist of the purchase or sale of financial derivatives, instruments such as futures contracts (agreements to buy or sell an asset at a fixed price on a certain future date) and options contracts (agreements giving the option to buy or sell the asset). Derivatives trading has the power to make huge sums of money, but ill-considered trading can lead to cataclysmic losses. In 1995, for example, Barings, Britain's oldest merchant bank, collapsed as the result of the transactions of a single "rogue" derivatives trader.

How do financial analysts determine the value of such a derivative? They turn to mathematical models, some of them quite intricate and sophisticated. Yet Dr. William Shaw, head of Financial Instrument Modelling in the Quantitative Analysis group of Nomura International, has determined that many of the standard textbook models used to direct a substantial fraction of the world's derivative transactions are flawed and do not accurately reflect financial realities.

"The real story," says Dr. Shaw, "is that derivative securities are capable of exhibiting some diverse forms of mathematical pathology that confound our intuition and play havoc with standard or even state-of-the-art algorithms."

His technique for unraveling these complexities relies heavily on the symbolic algebra capabilities of Mathematica, the same sophisticated technical computing system used by scientists and researchers worldwide to perform higher mathematics. Mathematica is a product of Wolfram Research, Inc.

The benefits of using Mathematica are quickly apparent says Dr. Shaw: "The whole range of analytical exotics can be coded up quickly from the fundamental research and used actively or in testing."

Dr. Shaw will present his findings and suggested remedies in the Financial Derivatives Seminars, a series of presentations in Frankfurt, Germany, on September 22; in London on September 24; and in New York on September 26.

An extensive discussion of his findings will also be given in Modelling Financial Derivatives with Mathematica, the forthcoming text to be published by Cambridge University Press.

Nomura International plc
Nomura International plc is the wholly owned European subsidiary of The Nomura Securities Co. Ltd, one of the world's largest investment banks. Its major activities in Europe include the origination, trading, and sales of securities; research; principal securitization; and emerging markets' corporate finance.

Wolfram Research, Inc.
Wolfram Research is the world's leading developer of technical computing software. The company was founded by Stephen Wolfram in 1987 and released the first version of Mathematica, its flagship product, on June 23, 1988. Mathematica, the world's only fully integrated technical computing system, is relied on today by more than a million users worldwide in industry, government, and education. Mathematica 3.0 was released in the fall of 1996. Wolfram Research, Inc. is headquartered in Champaign, Illinois.

Dr. William Shaw
Dr. Shaw has been working for Nomura International in London since 1992. He gained his B.A. in mathematics from King's College of the University of Cambridge in 1980 and his D.Phil. in mathematical physics from Oxford University in 1984. He subsequently held postdoctoral and teaching positions at Cambridge and MIT before beginning a career as a consultant to government and industry on diverse problems in applied mathematics.

He combines his career in mathematical finance with the teaching of applied mathematics at Balliol College, Oxford, and is working on his second book on the use of Mathematica. His first book, Applied Mathematica, was published by Addison-Wesley in 1993. He has published over 30 papers on topics ranging from asymptotically flat space-times, through string theory and diffusion models, to applied electromagnetics and computer algebra.