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If you completed the lesson on the implied volatility smile you have observed that even an out-of-the-money option will trade with a positive price.  The objective of this lesson is to understand why this is the case.

The intrinsic value of a call option is defined as the current underlying asset price minus the option's strike price and vice versa for a put option.

The difference between the market price of an option and it's intrinsic value is commonly referred to as the option's time premium.

In the US, stock options are American options, which means that they can be exercised at any time over their life.  Clearly, an American option, such as an option on IBM stock that is out-of-the-money, would never be exercised while it is out-of-the-money.  It can trade, however, for a positive price (i.e. premium), which implies a positive time premium.

In this lesson you will see that two major drivers of the time premium are the volatility of the underlying asset price and the length of time until the option matures.

Lets consider this for IBM options.  Firstly, fix the following inputs:

i.  The underlying asset's current price (i.e. IBM's stock price)

ii.  The option's strike price

iii.  The volatility of the underlying asset value

iv.   The risk free rate of interest

v.  The dividend yield for the underlying asset

You can enter or compute these as you have in earlier lessons.  If you feel comfortable with this then skip the inputs section and go to "The Time to Maturity Input" section below.

Inputs to the Option Calculator to the Left

To get i; leave the underlying ticker symbol as IBM or overwrite with IBM if this has been changed.  Next, click on the button - Get Stock Quote.  You will observe that the source web site (i.e. CBOE) comes up in the bottom right hand segment of your screen and the stock price data is extracted automatically for you.

Strike prices must be in intervals of 5 for IBM (i.e. 95, 100, 105, etc.).  Select the strike price to be approximately at-the-money.  That is, select the closest strike price in units of 5 to the current spot price of IBM.

Enter a volatility estimate for IBM.  In this lesson it is not important that your volatility estimate is accurate because we will be varying your initial estimate as part of the exercise.  Thus, you can enter 0.35 for IBM's volatility.

To get iv; select from the drop down menu (in the bottom input box) the first URL, Bloomberg's treasury.html, then double click on it.  You will observe the yield curve for US treasuries.  Enter the yield for the closest maturity on this yield curve to the box indicating Interest Rate (e.g. if the option matures in 1 month, copy the yield for 3 months because it is the closest duration of time and, therefore, the closest maturity).

Finally, to get v; select from the drop down menu Yahoo's finance page.  Enter IBM in the box titled Get Quotes and change basic to Detailed from the drop down menu beside this box on Yahoo's site.  You will now see under Yield the Dividend Yield for IBM.

The Time to Maturity Input

The option's maturity date is automatically computed for you by the calculator if you enter the month of expiration.  To select the option's maturity date look in the drop down box with the months listed, then select the most recent month first.  That is, you can select the current month so long as options are still trading.  A stock option expires on the Saturday after the third Friday of it's maturity date.  If today's date is after this date, then you must select next month as your maturity; otherwise select the current month.  To have the Option Calculator automatically compute the Maturity, you must then click on the button - Get Option Quote.

Final Checklist

Make sure you have selected 'American' for IBM stock options.  Virtually all stock options in the US are of the American style (i.e. can be exercised daily during the life of the option).  Also, check that you have selected a call option initially for this exercise.

Retrieving the Option Prices for Different Maturities

Enter IBM beside the Option Symbol box and then click on the button - Get Option Quote.

By clicking on Get Option Quote, the latest put or call price (which ever was selected) is automatically retrieved for you and entered into Market Option Price.

Required:

1.  Record the price and the option contract details.

You can do this simply with a spreadsheet by copying and pasting the results of each calculation to a spreadsheet or other application.  First, click inside the results section (e.g. value) and then right click the mouse to see the copy menu.  Now left click the mouse to copy the inputs to the window's clip board.  You can then paste this to your spreadsheet.

2.  Now select a new maturity holding all else the same.  That is, change the maturity by clicking on the next month and then click on Get Option Quote to get the next maturity.  Again, record or copy and paste your results.  Repeat for a third available maturity.

You should observe that the option's time premium for an at-the-money option will increase with time to maturity.  You can repeat this for other strike prices.

Why is this the case?

The longer the remaining life of your option the more likely it will be exercised in the future.  For example, if you have an American call option then you have the right to exercise it at any point in time during its life.  But once you exercise this right you pay \$K (the strike price).  You prefer to pay \$K at some future time than to pay \$K today; otherwise you give up the interest that could be earned on \$K today.  So your obligation is really the present value of \$K, which is less than your current obligation if exercised today.  The longer the time to maturity for an option the larger the difference between \$K today and the present value of \$K becomes.

Exploring the Drivers of the Time Premium

In Sensitivity we will take a closer look at these issues, but for the present you can explore the drivers of the option's time premium using the calculator.  For the default at-the-money, short maturity call option case above click on Calculate to compute the option's predicted price relative to the volatility you entered (i.e. 0.35).  You can observe whether your predicted price is greater than, or less than, the actual option's market price.

What does it mean if it is less than?

This implies that the implied volatility from the market price is greater than the volatility (0.35) that you entered into the calculator.  Similarly, if the predicted price is greater than the observed market price then the implied volatility from the market price is less than the volatility you entered into the calculator.

To check which is the case click beside Implied Volatility in the calculator and click on the Calculate button.  Now you can immediately compare the implied volatility from the market price with the volatility number you entered.

Thus you can see that the size of the time premium increases with the volatility of the underlying process.

Now turn off implied volatility.  That is, click in the check box beside implied volatility to turn it off.

You can see how you can easily calculate implied volatility yourself by trial and error - that is, keep changing the volatility number until the predicted price equals the market price.

Impact of Time on the Predicted Option Price

For the current example, you can observe how the predicted price of the option changes with the time to maturity.  Hit Calculate (with implied volatility turned off and the volatility number set to 0.35) to observe the predicted price of the IBM short maturity option.  Now select the next month for maturity from the drop down month menu (and click on the next month).  Next, click on calculate.  For the current IBM call option example you will see that the predicted price increases, which by definition implies that the time premium increases.

Alternatively, this increasing time premium insight implies that early exercise of an American call option is never desirable because, by exercising the option, you forgo a positive time premium.

By clicking on the Sensitivities button you will gain additional insights into option's time premium for both puts and calls.

OS Financial Trading System, PO Box 11356, Pittsburgh, PA 15238 USA, Phone 1-800-967-9897, Fax 1-412-967-5958, Email fts@ftsweb.com,

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