#### Stock Implied Volatility

Since you are a subscriber to our site, it is very likely that you’ve heard or used this term - "stock implied volatility". But did you ever notice the apparent inconsistency of the term? "Implied volatility" is a characteristic of a single option issue, with concrete expiry and strike price, not of an underlying of an option. In the real world, each option implies its own value of stock future volatility, different from the other option issues of this underlying - this is a well-known "implied volatility smile" phenomenon. However, there are different ways to "merge" individual options’ implied volatility into a composite number that can be interpreted as "stock implied volatility". The Implied Volatility Index is a value computed by IVolatility.com that represents "implied volatility of a stock".

#### Implied Volatility Index

On our site, you can find three different Implied Volatility Indexes (IV Index or IVX):

- IVX Call (calculated from Call options only)
- IVX Put (only Put options are used)
- IVX Mean (an average of the above)

Also, each variable is accompanied by a numerical index indicating the number of days for which IV Index is calculated, like IVX Call 30, IVX Mean 180, etc. The terms of 30, 60, 90, 120, 150 and 180 (calendar) days are available on our site. For example, IVX Call 30 value shows what volatility is implied by a hypothetical Call option with 30 days to expiry. This Call averages the characteristics of relatively more liquid Calls having their strike near the underlying spot price.

Now, what does the calculation of IV Index look like? Let’s see this on the example of "IVX Call 30". Suppose today is 04/05/2004, and there are 12 days till front month (April) expiry - and 47 days till next month expiry (May). Options with these two expiries will be used for IV Index calculation of term 30 - as they are 2 expiries closest to 30-day virtual expiration.

First, we take 4 April Call options contracts with strikes nearest to current stock price (spot) - they are used to calculate IV Index for April, or "IVX Call 12" (this value is used internally and not available on site for download). "IVX Call 12" is their weighted average, where weighting is by Vega (option price sensitivity to a change in Implied Volatility). Some of these options, however, can be considered "bad" and filtered out of further calculations. For example, options with expiry less than 1 week from now are always discarded. The other check is that so-called Put-Call parity relation should not vary significantly. This means that implied volatility values of Call and Put option in the pair are sufficiently close. Briefly, the filtering algorithm tries to eliminate suspicious option contract to make sure that the resulting IV Index figure is relevant.

In the very same way, the IV Index for May expiry is calculated, "IVX Call 47". Now, we interpolate these two values to get "IVX Call 30"; interpolation is linear by square root of days to expiry, that is,

This particular interpolation is commonly used when dealing with volatilities, as it better describes the local behavior of volatility (compared to linear by days to expiry interpolation).

#### What is "the" IV Index?

Well, as you see, there are many different IV Indexes - Call / Put / Mean, terms 30-180, and we were going to provide one number for "stock implied volatility", right ? The answer to this depends on the trading horizon you use; all other things being equal, we take "IVX 30 Mean" as "the" IV Index or a stock implied volatility. The reason is almost evident: the nearest expiry options are most liquid, so their implied volatilities are most relevant; Mean averages skew between Calls and Puts, if any.

#### Comparison to CBOE VIX®

Probably, you are aware of the most popular "market implied volatility" measure - CBOE VIX®, and recent enhancements (as of Sep 2003) to its calculation. VIX measures market expectation of near term volatility conveyed by stock index option prices. The New VIX is based on S&P 500 index option prices and incorporates information from the volatility "skew" by using a wider range of strike prices rather than just at-the-money series. One of its advantages, compared to our IV Index, is that VIX value is basically independent of the model used to derive implied volatilities - VIX is calculated as a weighted average of option prices. It is a relatively advanced topic, but indeed you can derive stock implied volatility without calculation of model-specific single option’s implied volatilities! Though, this can be done if you have a thick grid of strikes traded only. This is of course true for S&P 500, but not for the majority of optionable stocks. That’s why we stick to our model-dependent way of calculating IV Index - it allows us to calculate this measure for each individual stock, not for the market in general.

#### Usage of IV Index

That’s good to have stock implied volatility measure, but how it can be used in trading and risk management? See some suggestions on the topic in the next issue of newsletters!

Should you have any questions you can either write to us directly (support@ivolatility.com) or, if you think you question is worth public attention where more clients can also benefit , please use our ‘Methodology’ Forum:

http://www.ivolatility.com/forum.j?fid=5