Black-Scholes Equation

Black-Scholes Option Pricing Model

The 1997 Nobel Prize in Economic Science was awarded to Robert Merton and Myron Scholes for the Black-Scholes Option Pricing Model. Actually it was awarded “for a new method to determine the value of derivatives.” Sadly, Fisher Black had died in 1995 (just in his mid-fifties), and the Royal Swedish Academy of Sciences does not award the Nobel Prize posthumously. Although, up to three people can share the award together; the money is split equally, and each recipient gets their own medal. Their papers were published independently in 1973 in separate journals. Since the 1930’s, prior to these papers, the finance community was struggling to determine how to accurately model the value of an option and the minimum number of variables needed to do so.

In 1955, the finance community discovered a French graduate student’s Ph.D. thesis, published in 1900, and called The Theory of Speculation, by Louis Bachelier. This was the first person to describe the stochastic process of Brownian motion. Brown first observed this phenomenon in 1827, before atoms were well understood, and Einstein wrote a famous paper on Brownian motion for physicists in 1905. Bachelier’s work was not recognized at the level it deserved until the paper by Black and Scholes. Bachelier’s thesis advisor was the great mathematician and physicist, Henri Poincare. Because the thesis was not pure mathematics or physics and did not contain the level of mathematical rigor that was standard at the time, Bachelier did not receive high honors required to get an immediate offer professor at a European University. Bachelier held many teaching positions at many different universities throughout his life. His wife died not long after they were married, and World War I interfered with the continuity of his work, when he was drafted as a private in the French Army. Bachelier’s thesis actually discussed the use of Brownian motion to evaluate stock options, but he died...