CHAPTER 3

Options Pricing and Implied Volatility

One of the most fundamental questions for any investment concerns the price. Is it too expensive, or is it a bargain? In stock investments, one turns to price-to-earnings ratios, earnings growth rates, book values, and other measures to determine a stock’s worth. In 1973, Fisher Black and Myron Scholes published a theoretical model to price equity options. Robert Merton built upon that original paper with his work and was the first to refer to the pricing equation as the “Black-Scholes” options pricing model. In 1997, Merton and Scholes won the Nobel Prize in economics for this achievement. (Fisher Black was not eligible since he had died in 1995). This equation enabled investors to compute a quantitative measure of an option’s value and spurred the beginning of options trading on a large public scale. The Chicago Board Options Exchange was founded in 1973 and the Options Clearing Corporation began in 1977.

THE BLACK-SCHOLES PRICING MODEL

The Black-Scholes options pricing model is rather complex, but the calculations have been done for us on our brokerage platforms and in the options analysis software that is widely available. My point in displaying it here is to illustrate the relationships of the variables in the equation. The Black-Scholes pricing model calculates the price of a call option as (a similar equation calculates the put value):

where

Pc = the calculated, or theoretical, price of the call option d1 = d2 = s = the ...