V.6:10 (372-376): Black-Scholes vs. Cox-Ross-Rubinstein By John W. Labuszewski and John E. Nyhoff

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 model.

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.