What's an option worth?

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Theoretical Value (Fair Value) of an Option

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This information is provided for those who already have some understanding of options, but if you are a rookie, you would be better served to study this page after you understand the basic concepts) of options.  

The discussion on volatility has valuable background information that will help you become a better options trader. It's important to increase your understanding of options and the following discussion will make it easier for you to gain a good understanding of how options are priced in the marketplace.

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What is the theoretical value of an option and how is it determined?

When you buy or sell an option, a profit or loss results from that trade.  If you were to make that same trade under identical conditions many times, then the theoretical value (fair value) of the option is the price that would result your breaking even (excluding commissions).  In order to have an edge, the trader wants to buy options below their fair value, or sell them above the fair value.  If you consistently overpay for options, or sell them for too little, the probability of your making winning trades is diminished.

The value of an option is based on several factors. A pricing model is then applied to these factors to calculate the theoretical value. Such a pricing mechanism for options became widely available when Myron Scholes and Fisher Black developed the Black-Scholes model for pricing equity options. This occurred at about the time options began trading on an exchange (CBOE) in 1973. There have been refinements to this model over the years, but it is still in widespread use. In order to apply the model, the following data has to be input: 
    • stock price : The higher the stock price, the more a call is worth. (The less a put is worth.)
    • strike price :  The higher the strike price, the less a call ( the more a put) is worth.  The right to purchase the stock for a cheaper price is worth more than the right to buy it at a higher price.
    • time to expiration : The more time left before the option expires, the more any option is worth.
    • interest rate : The higher the interest rate, the more the call (less the put) is worth. This is because a call buyer uses less cash to buy the call than he would use to buy stock, and the difference can be invested to earn interest.  The more interest earned, the more a call buyer is willing to pay for the option.
    • dividend : An option holder is not entitled to cash dividends, and dividends reduce the price of the stock (when the stock goes ex-dividend, the stock price is decreased by the amount of the dividend).   The higher the dividend, the less a call is worth, and the more a put is worth.
    • volatility : The is the only one of the factors that is not known. (Of course dividends, interest rates, stock prices and time to expiration are constantly changing, but they are known at the time the option transaction is made.) The volatility used in the model is an estimate of the potential price movement that will occur during the life of the option. The higher the volatility, the more any option is worth because a high volatility increases the probability that the option will make a large favorable move for the holder of the option (Only a favorable move is considered, because if the move is unfavorable, the option holder loses nothing extra. Loss is limited to the price paid for the option.)   Since a change in the volatility estimate changes the value of an option by a lrge amount, and since this volatility a difficult factor to estimate, there is often a significant disagreement as to the fair value of an option.
Volatility, and how it applies to stock options, is frequently misunderstood.  In order to help those of you who are first learning about options to have a better understanding of this very important topic, a separate page is devoted to learning about volatility .

Are theoretical values of an option important for you?

If you are embarking on a strategy that is consistent over time, such as selling covered call options, then it is not necessary for you to be overly concerned with the theoretical value of an option each time you sell options.  The reason is that sometimes you will receive more than an option is worth when you sell it, and at other times, you will receive less than it is worth.  Over an extended period of time, this should result in your receiving an approximation of fair vailue for the options you sell.

If you are considering buying or selling options on an irregular basis, then the price at which your transaction occurs is of much greater importance.  A discussion of why this is true follows.

Before we get to that, this is an appropriate time to point out that we strongly recommend conservative options strategies.  Although the more speculative strategies involving stock options are capable of producing some very exciting returns, most of the time they result in a loss of money. Frequently, that loss is 100% of the capital invested in the position.  We feel so strongly about recommending a conservative approach when using stock options, we have written a book on the subject. 

Why theoretical values are important

Trading an option without regard to its theoretical value, or how that value is determined, is giving up your best chance to become a successful trader. Of course, if you know for certain which way a stock is going to move, then it probably does not matter that you pay far more for an option than it is worth.  For those of us without such insight, being aware of the fair value of an option is essential.
Trading with knowledge of theoretical values can save a trader large amounts of money over his trading career. Sometimes you can enter an order to buy or sell an option and the premium paid (or received) will be reasonable. There are often times however, when the premium levels are extremely high or low. This can occur when a major news event, such as an earnings report, is pending (premiums are high), when the market in the stock has been dull and no news is expected (premiums are low), or even when a person with a major influence on market movement (Federal Reserve chairman, for ex.) is about to make a statement. Thus it is not a good idea to assume that options are always reasonably priced. There are times when the expectation is universally high that a major move in the entire market is either imminent, or has just occurred. When a major move has occurred, there is an increased chance that an additional major move is imminent.  At those times, option premiums reach very high levels, when compared with historical standards. A trader who generally buys options has to decide whether it is right to pay these very high premiums or to sit on the sidelines and wait for a better oportunity.  Similarly those who generally sell options have to decide whether to be fully invested when option prices are at historically low levels, or to reduce their trading and wait. Sellers of uncovered options also have to be concerned the market may make a major move in either direction, exposing them to large potential losses.
Knowing how to use option theoretical values can guide the trader (after he chooses a particular stock) in selecting which particular option to buy or sell. The observation that one specific option  series is much more overvalued (or undervalued) than others can help a trader initiate a position that not only allows him/her to have the long or short position he wants, but to do so with the extra edge that comes from having the position at a favorable price.
If any of the terms in the above discussion are not clear to you, see the glossary  
Even though there is a model to calculate the theoretical value of an option, there is often a great difference of opinion on what the fair value of an option is.  It is this difference of opinion that helps to create a marketplace.
Use the calculator:

There are several online sites that provide an 'options calculator'.   We provide our own, couresty of Dr. Robert Lum. The calculator provided here is sufficient for most users.  

I recommend the calculator offered at no cost by the CBOE.

DISCLAIMER: Any gains or losses that result of use, misuse or non-use of the information provided is the sole responsibility of the user.