CBOE Index Workbench

BACKGROUND ON VOLATILITY CONCEPTS AND DEFINITIONS

With regard to stock prices and stock index levels, volatility is a measure of changes in price expressed in percentage terms without regard to direction. This means that a rise from 200 to 202 in one index is equal in volatility terms to a rise from 100 to 101 in another index, because both changes are one percent. Also, a one percent price rise is equal in volatility terms to a one percent price decline. While volatility simply means movement, there are four ways to describe this movement:

1. Historic Volatility

Historic volatility is a measure of actual price changes during a specific time period in the past. Mathematically, historic volatility is the annualized standard deviation of daily returns during a specific period.

2. Future Volatility

Future volatility means the annualized standard deviation of daily returns during some future period, typically between now and an option expiration. And it is future volatility that option pricing formulas need as an input in order to calculate the theoretical value of an option. Unfortunately, future volatility is only known when it has become historic volatility. Consequently, the volatility numbers used in option pricing formulas are only estimates of future volatility. This might be a shock to those who place their faith in theoretical values, because it raises a question about those values. Theoretical values are only estimates, and as with any estimate, they must be interpreted carefully.

3. Expected Volatility

Expected volatility is a trader's forecast of volatility used in an option pricing formula to estimate the theoretical value of an option. Many option traders study market conditions and historical price action to forecast volatility. Since forecasts vary, there is no specific number that everyone can agree on for expected volatility.

4. Implied Volatility

Implied volatility is the volatility percentage that explains the current market price of an option; it is the common denominator of option prices. Just as p/e ratios allow comparisons of stock prices over a range of variables such as total earnings and number of shares outstanding, implied volatility enables comparison of options on different underlying instruments and comparison of the same option at different times. Theoretical value of an option is a statistical concept, and traders should focus on relative value, not absolute value. The terms "overvalued" and "undervalued" describe a relationship between implied volatility and expected volatility. Two traders could differ in their opinion of the relative value of the same option if they have different market forecasts and trading styles.

Options involve risk and are not suitable for all investors. Prior to buying or selling options, a person must receive a copy of Characteristics and Risks of Standardized Options, which is available from The Options Clearing Corporation, One North Wacker Dr., Suite 500, Chicago, IL 60606, or by calling 1-888-OPTIONS.

Please note that futures on the CBOE Volatility Index® (VIX®) were introduced in 2004 after the methodology for VIX was changed; please visit www.cboe.com/vix for volatility updates that might not be reflected on this CD-ROM.

This discussion is designed to assist individuals in learning how options work and in understanding various options strategies. This discussion is for educational purposes only and is not intended to provide investment advice. Commissions, taxes and transaction costs generally are not included in the strategy discussions, but can affect final outcome and should be considered. Please contact a tax advisor for the tax implications involved in these strategies.
This discussion has been prepared solely for informational purposes, based upon information generally available to the public from sources believed to be reliable, but no representation or warranty is given with respect to its accuracy or completeness. No statement herein should be construed as a recommendation to buy or sell a security or to provide investment advice. Any profit/loss diagrams refer only to approximate results at expiration. Past performance is no guarantee of future results.

S&P 100® and S&P 500® are registered trademarks of the McGraw-Hill Companies, Inc., and are licensed for use by the Chicago Board Options Exchange, Inc. ("CBOE"). The Russell 2000® Index is a registered trademark of Frank Russell Company. The Nasdaq 100® is a registered mark of The Nasdaq Stock Market, Inc. "Dow Jones SM", "Dow Jones Industrial AverageSM", "Dow Jones Transportation AverageSM," and "Dow Jones Utility AverageSM" are service marks of Dow Jones & Company, Inc. and have been licensed for certain purposes by the CBOE. iSharesSM is a servicemark of Barclays Global Investors. The Goldman Sachs Technology Indexes are the property of Goldman, Sachs & Co. and have been licensed to the CBOE in connection with the trading of options based upon the indexes. Dow Jones & Co., The Nasdaq Stock Market, Goldman Sachs, and McGraw-Hill make no warranties and bear no liability in regard to the trading of index options.VIX®, CBOE Volatility Index® LEAPS®, FLEX®, FLexible EXchange® and OEX® are registered trademarks and Long-term Equity AnticiPation SecuritiesTM and SPXTM are trademarks of the Chicago Board Options Exchange, Inc.

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