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VALUING AN OPTION
Options let you trade volatility directly. In the previous two lessons you learnt how to back out the volatility implied from an option price and how to estimate the implied volatility from options with nearby strike prices holding all other contractual features constant.
In this lesson we answer the following question.
Question: How do I calculate the value of an option using the volatility implied from options with nearby strike prices.
To calculate an option's value we need the following inputs:
i. The underlying asset's current price (i.e., IBM's stock price)
ii. The option's strike price
iii. The option's maturity date (the date the option expires)
iv. The underlying asset's volatility
v. The risk free rate of interest
vi. The dividend yield for the underlying asset
You can compute the option price by completing the following steps using the Option Calculator beside this lesson:
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.
If you have just completed Calculating the Implied Volatility Smile lesson then enter the option's Strike Price to approximately equal IBM's current stock price less $5 (i.e., K - 5 in the previous lesson where K is the at-the-money strike price. Strike prices must be in intervals of 5 for IBM (i.e., 95, 100, 105, etc.,) which is why K will only approximately equal the current stock price. If you are not following on from the previous lesson then you can enter a strike price of your choice.
To get iii. look in the drop down box with the month's listed, then select the month in which you would like your option to mature. This should match the month you selected in previous lesson, or otherwise use the maturity month of your choice. If in doubt about valid maturities select one month later than the current month. To get the Option Calculator to automatically compute the maturity you must also click on the button Get Option Quote.
Now the important step iv. for valuing an option which requires that you enter your estimate for volatility. In the previous lesson you learnt how to estimate this using option prices from options with nearby strikes. Of course you can also estimate it using other sources (e.g., forecasts from historical volatilities or other data sources).
To get v. select from the drop down menu (in the bottom input box) the first URL, Bloomberg's treasury.html and 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 vi. select from the drop down menu Yahoo's finance page. Then 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.
This has now completed all input requirements for valuing the IBM option.
Check that 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 on any day during the life of the option). Also check that you have selected the appropriate type of option (put or call).
Make sure the box beside Implied Volatility is blank (i.e., uncheck this box if checked by clicking in it).
Calculating the Option Price
You can now click on the button Calculate to see the predicted option price for your IBM option. This number will appear next to the Calculate button.
Exploring the Drivers of the Option Price
First, once you have computed price change volatility. Suppose you increase volatility and then click Calculate you will see that the option price increases with an increase in volatility. Furthermore, try this out for both a put and a call. You will see that in both cases the option price increases with an increase in volatility.
Second, you are encouraged to make small changes to all other inputs to see how it impacts upon the option price.
In the next lesson we will learn about the intrinsic value of an option versus the time premium.
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