# A Primer on Option Pricing

Of the various ways to value an option, probably the most widely known method is the Black-Scholes pricing model. This approach to valuing options was detailed in

*The Pricing of Options and Corporate Liabilities*

, a research paper by Fischer Black and Myron Scholes that was first published in 1973.

The Black-Scholes model can be complex, but for our purposes we'll focus on the five components that go into calculating an option's theoretical value: the price of the underlying asset, the strike price of the option, the expiration date, prevailing short-term interest rates and the

*expected*

volatility of the underlying asset.

The most important component in options trading is volatility. The expected, or implied, volatility is closely tied to the historical price movement of the underlying asset.

Because historical movements can be collected and analyzed, traders can use that information to make certain assumptions about how the option will react relative to the underlying asset. Therefore, implied volatility, which is theoretical and predictive in nature, is the X factor in valuing an option. Often, it's the difference between making and losing money.

Historical volatility is calculated using the annualized standard deviation of the daily percentage change in the price of a given asset. In other words, it's based on past patterns of price movement over a given period of time. This number's accuracy will increase over time as more data points are collected. The

*fair value*

of an option is calculated on the basis of the historical volatility of an underlying asset.

As an example, let's look at options on

## TheStreet Recommends

**General Electric**

(**GE**) - Get General Electric Company Report

. The stock opened Thursday at $24.60, and the December 25 call was trading at $1.25.

In this example, we know several of the components needed to make a judgment about the option. Because we have the price of the current option, the underlying asset (GE's stock), the option's strike price (25) and the expiration date (December), we can use the Black-Scholes method to arrive at the implied volatility. In this case, it's 43.92.

This is slightly on the expensive side, given that during the last five years the average volatility for GE at-the-money calls is 35, which also happens to be where the current overall market volatility (as measured by the

CBOE Volatility Index, or VIX), is standing.

Using a volatility of 35, the GE December 25 call would have a theoretical value of 97 cents. For comparison, if we plug in an implied volatility of 60, often considered a panic level, the call would then be assigned a theoretical value of $1.75.

The issue of historical vs. implied volatility gets to the heart of whether a given option seems cheap or expensive when measured against the underlying asset's past trading behavior. Options trade using implied volatility, which, as indicated above, is theoretical and predictive in nature. If you decide a current price is out of whack or without precedent, you may try to profit from it.

If you want to understand more about how different components affect option prices, you can run through various scenarios using one of the many option tools available online. The

**Chicago Board Options Exchange's**

Web site is a good resource and has a

calculator you can use.

Steven Smith writes regularly for TheStreet.com. In keeping with TSC's editorial policy, he doesn't own or short individual stocks. He also doesn't invest in hedge funds or other private investment partnerships. He invites you to send your feedback to

Steve Smith.