# Option Pricing Theory

## What it is:

**Option pricing theory** is the theory of how options are valued in the market. The Black-Scholes model is the most common option pricing theory.

## How it works (Example):

All options are derivative instruments, meaning that their prices are derived from the price of another security. More specifically, options prices are derived from the price of an underlying stock. For example, let's say you purchase a call option on shares of Intel (INTC) with a strike price of $40 and an expiration date of April 16. This option gives you the right to purchase 100 shares of Intel at a price of $40 on or before April 16th (the right to do this, of course, will only be valuable if Intel is trading above $40 per share at that point in time).

Accordingly, the price of an option is a factor of the current price of the underlying security (the Intel stock), how long you have to exercise the option, how volatile Intel stock tends to be, and the price you’d have to pay to exercise your option (the strike price). Figuring out what the price of an option "ought to be" is like trying to predict the weather with 100% accuracy.

The most common way to do this is to use the Black-Scholes model, named after Fischer Black and Myron Scholes, who developed it in 1973. (Robert Merton also participated in the model’s creation, and this is why the model is sometimes called the Black-Scholes-Merton model.)

## Why it Matters:

The basic mission of option pricing theory is to calculate the probability that an option will expire in the money. To do this, the Black-Scholes model looks beyond the simple fact that the value of a call option increases when the underlying stock price increases or when the exercise price decreases. Rather, the model assigns value to an option by considering several other factors, including the volatility of Company XYZ stock, the time left until the option expires, and interest rates.

For example, if Company XYZ stock is considerably volatile, there is more potential for the option to go in the money before it expires. Also, the longer the investor has to exercise the option, the greater the chance that an option will go in the money and the lower the present value of the exercise price. And higher interest rates raise the price of the option because they lower the present value of the exercise price.

No theory is perfect, however. Empirical studies do show that the Black-Scholes model is a very predictive options pricing theory, meaning that it generates option prices that are very close to the actual price at which the options trade. But various studies also show that the model tends to overvalue deep out-of-the-money calls and undervalue deep in-the-money calls. It also tends to misprice options that involve high-dividend stocks.