Price vs Value-How Traders Use Option-Pricing Models

Like in the common-life example just discussed, the right to buy or sell an underlying security—that is, an option—can have value, too. The specific value of an option is determined by supply and demand. There are several variables in an option contract, however, that can influence a trader’s willingness to demand (desire to buy) or supply (desire to sell) an option at a given price. For example, a trader would rather own—that is, there would be higher demand for—an option that has more time until expiration than a shorter-dated option, all else held constant.

And a trader would rather own a call with a lower strike than a higher strike, all else kept constant, because it would give the right to buy at a lower price.Several elements contribute to the value of an option. It took academics many years to figure out exactly what those elements are. Fischer Black and Myron Scholes together pioneered research in this area at the University of Chicago.

Ultimately, their work led to a Nobel Prize for Myron Scholes.Fischer Black died before he could be honored.In 1973, Black and Scholes published a paper called “The Pricing of Options.The Black-Scholes model values European call options on non-dividendpaying stocks. Here, for the first time, was a widely accepted model illustrating what goes into the pricing of an option. Option prices were no longer wild guesswork.

They could now be rationalized. Soon, additional models and alterations to the Black-Scholes model were developed for options on indexes, dividend-paying stocks, bonds, commodities, and other optionable instruments. All the option-pricing models commonly in use today have slightly different means but achieve the same end: the option’s theoretical value.

For American-exercise equity options, six inputs are entered into any option-pricing model to generate a theoretical value:stock price, strike price, time until expiration, interest rate, dividends,and volatility.Theoretical value—what a concept! A trader plugs six numbers into a pricing model, and it tells him what the option is worth, right? Well, in
practical terms, that’s not exactly how it works. An option is worth what the market bears.

Economists call this price discovery. The price of an option is determined by the forces of supply and demand working in a free and open market. Herein lies an important concept for option traders: the difference between price and value.Price can be observed rather easily from any source that offers option quotes (web sites, your broker, quote vendors, and so on). Value is calculated by a pricing model.

But, in practice, the theoretical value is really not an output at all. It is already known: the market determines it. The trader rectifies price and value by setting the theoretical value to fall between the bid and the offer of the option by adjusting the inputs to the model.Professional traders often refer to the theoretical value as the fair value of the option.At this point, please note the absence of the mathematical formula for the Black-Scholes model (or any other pricing model, for that matter).

Although the foundation of trading option greeks is mathematical, this book will keep the math to a minimum—which is still quite a bit. The focus of this book is on practical applications, not academic theory. It’s about learning to drive the car, not mastering its engineering.The trader has an equation with six inputs equaling one known output.

What good is this equation? An option-pricing model helps a trader understand how market forces affect the value of an option. Five of the six inputs are dynamic; the only constant is the strike price of the option in question. If the price of the option changes, it’s because one or more of the five variable inputs has changed.

These variables are independent of each other, but they can change in harmony, having either a cumulative or net effect on the option’s value. An option trader needs to be concerned with the relationship of these variables (price, time, volatility, interest). This multidimensional view of asset pricing is unique to option traders.