Credit: Shutterstock photoIn today's edition of Options Basics, we're going off the beaten path to learn how options are priced using the Black Scholes Formula . 
More than 30 years ago, Fischer Black, Robert Merton, and Myron Scholes took the guesswork out of options pricing by publishing the Black Scholes formula, which values an option as a function of the following elements: stock price and strike price, time until expiration, volatility, dividend status, and interest rates.
Stock Price and Strike Price
It may sound obvious, but the most important factor that determines the price of an option is the underlying stock price relative to the strike price of the option. As a stock ticks higher, the price of a call will likely increase, while the price of a put will most likely drop. Conversely, as a stock gravitates lower, the price of a call will likely subside, while the price of a put will typically become more expensive.
The relationship between the underlying stock price and the strike price determines whether an option is in the money or out of the money. The relationship also quantifies an option's intrinsic value , which is the amount by which an option is in the money. In other words, intrinsic value is: the amount by which a stock price exceeds the strike price of a call; or, the amount by which a stock price falls below the strike price of a put.
For example, let's say that Stock ABC is trading at $50. The ABC 45 call would have an intrinsic value of $5 ($50 - $45 = $), as would the ABC 55 put ($55 - $50 = $5). However, the ABC 55 call and ABC 45 put would both have an intrinsic value of zero, since they're currently out of the money.
Time until Expiration
The passage of time - known as time decay - works against an option buyer, as the price of out-of-the-money options decreases at an accelerating rate as expiration approaches. For this reason, back-month options will typically be more expensive than front-month options, since further-dated contracts have more time to end up in the money.
Using our previous example, let's say the shares of ABC are still trading near $50. With this in mind, an ABC June 60 call would most likely be less expensive than an ABC September 60 call, even though both contracts have the same strike. This is because the September position has more time until expiration, thus, a better chance of finishing in the money.
To calculate an option's time value, you would subtract the intrinsic value from the price of the option. Earlier, we established that the intrinsic value of the ABC 45 call was $5. Now, let's assume that the last ask price of this in-the-money option was $7.50. In this case, the ABC 45 call's time value would be $2.50 ($7.50 - $5 = $2.50).
Volatility
Volatility reflects the propensity of the underlying stock to fluctuate either up or down. Traders often take into consideration a security's historical volatility, which measures the stock's past movements, and implied volatility , which measures what options players expect future volatility will be. Simply put, a stock that tends to fluctuate more relative to another stock will command higher premiums.
For example, we know that Stock ABC is trading near the $50 level; as a result, let's say the at-the-money ABC 50 call is going for $5. Now, let's say that Stock XYZ is also trading near the $50 level - wouldn't that make the price of an XYZ 50 call $5, too? Not necessarily.
Though the shares of ABC and XYZ are both trading near the $50 level, XYZ could have a higher historical volatility. Simply put, the shares of XYZ could be more prone to fluctuate in the past, making the chances greater for an at- or out-of-the-money option to finish in the money.
Dividends and Interest Rates
Though the aforementioned factors generally have a greater impact on option prices, dividend and interest rates can also take a toll.
Since paying out a dividend reduces the stock price by the amount of a dividend, larger dividends tend to decrease call prices and increase put prices. This is because dividends increase the attractiveness of holding the stock rather than buying calls on the stock. Conversely, short sellers must pay out dividends, so purchasing puts is more attractive than shorting a stock.
Meanwhile, escalating interest rates increase call premiums and decrease put premiums. Higher rates increase the underlying stock's forward price, which is assumed by the model to be the value of the stock at option expiration.
Schaeffer's Investment Research Inc. offers real-time option trading services, as well as daily, weekly and monthly newsletters. Please click here to sign up for free newsletters. The SchaeffersResearch.com website provides financial news, education and commentary, plus stock screeners, filters and many other tools. Founder Bernie Schaeffer is the author of the groundbreaking book, The Option Advisor: Wealth-Building Techniques Using Equity & Index Options .
The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.
All Rights Reserved. Unauthorized reproduction of any SIR publication is strictly prohibited.
The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.
