The Fair Market Value Calculator is a web based tool that allows you to calculate an option's theoretical fair value - no download is required. Based on the criteria you enter, the calculator uses an adjusted Black-Scholes option pricing model to estimate the theoretical value of both the call and put option with the chosen strike price. This can help you determine if a particular option is over-valued, under-valued, or trading at fair value. An example of the calculator, with all the fields filled in, is shown in Figure 1
Figure 1: Example using the January 37.5 GE stock option
There are a number of fields that you are required to fill in before a value can be calculated. A change in any one of these variables may affect the value of a particular option. The example above to determine the fair value for the call and put options with a strike price of 37.5 for General Electric (Symbol: GE, currently trading at $37.14). Let’s look at exactly what each of these individual fields is asking for. Along the way, I will tell you what input is needed as well as its probable impact on the fair value calculation.
Type of Underlying
Click on the down arrow to see three choices in the drop down menu - Stock, Index or Future. Simply choose the appropriate one for the asset you are interested in.
Type of Option
Clicking on the down arrow reveals two choices - American-Style or European-Style. American-Style options are exercisable at any time between now and the expiration date. This ability should make them more valuable than European-Style options, which can be exercised only on the last day of trading prior to expiration. You should check the contract specifications on the exchange if you are unsure which to choose.
Expiration Date/Days to Expiration
Only one of these two fields needs to be entered. If you input a specific expiration date, the number of days is automatically calculated and displayed. If you input the number of days, the Expiration Date field will automatically be populated. All other things being equal, the longer the time period until expiration, the more valuable an option will be.
Option Strike Price
This is the predetermined price at which the option can be exercised, and it must be entered in decimal format (i.e. 17.50). Stock options were traditionally available in $2.5 increments below $25 and in $5 increments above $25. This calculator allows you to input any strike price, enabling the calculator to handle not only the various indexes and futures but also special stock options that might be granted privately by a company or any customized Over-the-Counter (OTC) options.
Underlying Price
Here you should input the current price of the underlying stock, index, or future. Taken together, the Underlying Price and Option Strike Price fields have a significant effect on the value of the call and put options. Deep in-the-money (ITM) options (with a strike price lower than the underlying price for calls, higher than the underlying price for puts) will have a value that approaches the underlying price. Far out-of-the-money (OTM) options (with a strike price higher than the underlying price for calls, lower than the underlying price for puts) will have a value that approaches zero the farther away from the current price you go.
Volatility
The Underlying Price (vs. the Strike Price), Time (to expiration) and Volatility are the three most important factors in determining the value of an option. All other things being equal, increasing the volatility input here will increase the value of both the call and put option, while a lower volatility number will decrease the value of both the call and put. The volatility number required for this field is a percentage, normalized to one year.
Knowing what to input into this field is the usually the most difficult decision users of this fair value calculator have. What should be input in this field is the expected future volatility of the asset. Naturally, no one knows exactly what the volatility of an asset will be in the future, but forecasting future volatility is the key to accurate option pricing and there are a couple methods we can suggest you use to find an appropriate number.
Most online brokers, especially those that specialize in options, calculate and display Statistical Volatility (the actual volatility of the asset) as well as the implied volatility of each individual option. The "purest" method of measuring volatility is by statistical analysis of the recent price history of the asset itself. However, implied volatility is usually considered to be a better indication of future volatility, because options are priced to reflect the market’s expectations for future volatility of the underlying asset.
Dividend Yield
This is an optional field, used primarily for stocks and indexes. It is optional since many stocks, and all futures, do not pay dividends. The field asks for an annualized percentage yield. Like much of the information required for an option calculator, it would be input the futures dividends that will be paid. But since that is not usually known, the history of past dividends is usually a reliable guide. All the major free financial websites calculate and display the dividend yield for indexes and stocks that pay dividends.
You can also calculate the annualized percentage yield yourself by looking up the past dividend pattern and payouts. In the example shown, GE paid a dividend each quarter of $0.28. So in one year it paid out 4 x $0.28 = $1.12. Divide that by the current price of $37.14 and you get an annualized dividend yield of 3%. Cash dividends affect option prices through their effect on the underlying price.
Because the stock price is expected to drop by the amount of the dividend, high cash dividends imply lower call premiums and higher put premiums. While the stock price itself usually undergoes a single adjustment by the amount of the dividend, option prices anticipate dividends that will be paid. That is why dividends should always be taken into account when calculating the fair value of an option
Risk-Free Interest Rate
Another optional field is the interest rate. In this field you should input the current quoted interest rate on a US Treasury bill, note or bond that most closely corresponds to the length of the period being analyzed. This field defaults to 2%, although I changed it to the current one month T-Bill rate of 2.86% in the example shown.
An increase in interest rates will drive up the value of calls and cause put premiums to decrease. To understand why, think about the effect of interest rates when comparing an option position to simply owning the stock. It is much cheaper to buy a call option than 100 shares of stock, and the call buyer can invest the difference in the capital required between the two positions. When interest rates are low, like they are now, they have only a minimal effect on option prices.
How Accurate is the Fair Market Value Calculator?
Once you have completed filling in all the fields, click the "Go" button. The Put and Call Fair Market values are then calculated and displayed at the bottom. In the GE example shown the calculator displays a value of $1.10 for the call option and $1.47 for the put option. So how do these values compare to the prices being quoted in the market?
As you can see, the calculated fair values are in line with the quoted Bid (the price someone is willing to sell it for) and Asked (the price someone is willing to buy it for). This example shows how accurate the fair market value calculator really is, given the proper inputs. The formula for the Black-Scholes option pricing model, which is the basis for the model used by virtually all traders, is widely available in many books and publications.
The original work by Black and Scholes was only done on European-Style equity call options. But since their work was originally published, extensions of their model have been developed, including the Yates model used in this calculator, which allows you to price American-Style options and takes into account dividends and the possibility of early exercise for puts. If you are interested in learning more about the exact mathematical formulas used to calculate option values, I would recommend the book Option Volatility and Pricing Strategies by Sheldon Natenberg.
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