Wall Street applauds formula that cracks "American options" problem

Jun 01, 2007

University of Wollongong mathematician, Professor Song-Ping Zhu, who has cracked a formula that will have important implications for researchers, traders and investors working on the valuation of American-style stock options, has presented his findings to the financial centre of the world, New York, to resounding acclaim.

Professor Zhu was invited to give a presentation in the Mathematics Finance Seminar Series at the Courant Institute of Mathematical Sciences, which is part of New York University. Courant Institute of Mathematical Sciences is the best-known mathematical institute in the world and the seminar series held at the Courant Institute is regarded by many mathematicians as the most prestigious series in mathematical finance.

Dr Sateesh Mane who works in the private finance sector in New York described Professor Zhu's work as an "elegant solution" and said the seminar at the Courant Institute was "one of the best I have ever attended".

"He clearly and succinctly explained not just his work, but the general context of the problem. I have every expectation that he (Professor Zhu) holds great promise of many more successful accomplishments," Dr Mane said.

Dr Richard Farber, a Vice President of American Stock Exchange, Equities Options ETFs, commented on Professor Zhu's seminar, saying: "I look forward to seeing more interesting and ground-breaking work from you."

Others who have lauded the presentation include Professor Peter Carr who is the Head of Quantitative Financial Research at Bloomberg LP and Director of the Masters in the Maths Finance Program at Courant Institute and Professor Marco Avellaneda who is the Organiser of the Math Finance Seminar Series and the Director of Mathematical Finance at the Courant Institute of Mathematical Sciences. Both are world-renowned figures in the area of financial mathematics.

Options are financial derivatives popularly used by companies and large financial institutions in their risk management. Their valuation is, however, a quite complicated process as the value of an option depends on, among many other factors, the underlying asset (such as stock) value, the time left for the option contract to expire, the strike price at which the option can be exercised, the interest rate, and the volatility that measures the market fluctuations.

The valuation of options was never a simple job until two mathematicians/economists, Fischer Black and Myron Scholes, derived a mathematical equation (widely referred to as the Black-Scholes equation) in 1973 to guide the pricing of options and many similar financial derivatives. The formula derived by Fischer Black and Myron Scholes as an exact solution of the Black-Scholes equation has been widely accepted by the financial market as a guide for pricing the so-called European options. Over time the significance of their discovery was fully recognised and in 1997 the Nobel Prize for Economics was awarded to Myron Scholes and Robert Merton. (Merton worked in a similar area at about the same time. Black died in 1995 and Nobel Prizes are not awarded posthumously). However, in today's financial markets worldwide, popularly traded stock options are of American style. Unlike European options, American options can be exercised at any time prior to expiry.

Mathematicians worldwide have been working for years to find an exact solution of the Black-Scholes equation for the valuation of American options -- many concluded that such a solution did not exist - until now with Professor Zhu's newly-found exact solution of the Black-Scholes equation for American options. Professor Zhu has had his journal paper, "An Explicit and Exact Solution of the Value of American Put and its Optimal Exercise Boundary" publicised in the journal, Quantitative Finance.

For further information contact Professor Song-Ping Zhu on (02) 4221 3807; 0403 854 998 (m); or spz@uow.edu.au

For more information, contact:

media@uow.edu.au
University of Wollongong
Ph: (02) 4221 5942; fax (02) 4221 3128