Tuesday, May 02, 2006

Song-Ping Zhu Has Found An Exact Solution for the Black-Scholes Equation


Prof. Song-Ping Zhu at University of Wollongong, Austrialia, has recently found another exact solution of celebrated Black-Scholes equation that corresponds to the so-called American option, which has long been regarded as an outstanding problem in finance mathematics modeling, and it has been hailded as a holy grail in mathematics.

The so-called Black-Scholes equation derived by Fischer Black and Myron Scholes in 1973 is the mathematical model for valuation of option. Prior to Zhu's solution, the only existing exact solution of Black-Scholes equation was the solution corrsponding to the so-called European option, which was found by Fischer Black and Myron Scholes in 1970s. This solution has been widely accepted by the financial market as a guide for pricing for the European options. Over time the significance of their discovery was fully recognized, 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 options are of American style. Unlike European options, American options can be exercised at anytime prior to expiry.

Zhu's findings have triggered widespread excitement among his mathematical colleagues who are confident that this long-standing problem has finally been solved. Professor Zhu has now had his journal paper, “An Explicit and Exact Solution of the Value of American Put and its Optimal Exercise Boundary” accepted for publication in the journal, Quantitative Finance.
(See the press release).

Added Notes: Prof. Song Ping Zhu, my childhood friend, is a fluid mechanician, who obtained a PhD degree in applied mechanics in late 1980s from University of Michigan at Ann Arbor. Dr. Zhu is the last PhD student of the late Professor Chia-Shun Yih.

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