Black-Scholes vs. Cox-Ross-Rubinstein
By John W. Labuszewski and John E. Nyhoff
Professors Fischer Black and Myron Scholes of the University of Chicago introduced, in 1973, what
was to become the most commonly cited option pricing model. This was a fortuitous beginning because it
roughly coincided with the introduction of exchange-traded stock options on the Chicago Board of
Options Exchange (CBOE). A few years later, Professors John Cox, Stephen Ross and Mark Rubinstein
introduced another pricing model which now enjoys popularity second only to the Black-Scholes model.
Both models produce similar results because they are very similar. In fact, the Cox-Ross-Rubinstein
model represents a logical precursor to the Black-Scholes model, despite the fact that the Black-Scholes
model was introduced earlier in a chronological sense. In order to gain an intuitive understanding of the
Black-Scholes model, we will start by describing the concepts underlying the Cox-Ross-Rubinstein
Underlying price distribution
Assume that the price of bonds is at 100% of part. What is the fair-market value of a call struck at 100?
In order to address that question, let us review the concept of fair-market value:
The fair-market value of an option is the premium at which both buyer and seller expect to break
even in a statistical sense, i.e., over a large number of trials.