# How is options implied volatility for a stock determined?

For any given stock in Interactive Broker's TWS (and I bet with any other broker), there is an option's historical volatility and an option's implied volatility. I know the historical volatility is the annualized standard deviation of the stock. But how is the implied volatility determined?

I am aware that the implied volatility is the volatility the market expects in the future. But how far in the future? Is it the implied volatility using options that will expire in one year? Is it the implied volatility using options of expiry of one month? Is it determined using at-the-money or in-the-money options? Is it the average implied volatility of all the options?

I don't need to know the mathematical model used (if it's based on Black Scholes or not). I would just like to know some general information about how the stock's IV is determined. i.e What options with what strike prices and expiry dates are used to determine the IV?

There are a few different "kinds" of implied volatility. They are all based on the IVs obtained from the option pricing model you use.

(1) Basically, given a few different values (current stock price, time until expiration, right of option, exercise style, strike of the option, interest rates, dividends, etc), you can obtain the IV for a given option price. If you look at the bid of an option, you can calculate the IV for that bid. If you look at the ask, there's a different IV for the ask. You can then look at the mid price, then you have a different IV, and so on and so on. And that's for each strike, in each expiration cycle! So you have a ton of different IVs.

(2) In many option trading platforms, you'll see another kind of IV: the IV for each specific expiration cycle. That's calculated based on some of the IVs I mentioned on topic (1). Some kind of aggregation (more on this later).

(3) Finally, people often talk about "the IV of stock XYZ". That's, again, an aggregation calculated from many of the IVs mentioned on topic (1).

Now, your question seems to be: which IVs, from which options, from which months, with which weight, are part of the expiration cycle IV or for the IV of the stock itself?

It really depends on the trading platform you are talking about. But very frequently, people will use a calculation similar to how the CBOE calculates the VIX. Basically, the VIX is just like the IV described on topic (3) above, but specifically for SPX, the S&P 500 index.

The very detailed procedure and formulas to calculate the VIX (ie, IV of SPX) is described here: http://cfe.cboe.com/education/vixprimer/about.aspx

If you apply the same (or a similar) methodology to other stocks, you'll get what you could call "the IV of stock XYZ".

Option pricing models have 6 variables:

Underlying price

Time until expiration

Strike price

Volatility

Carry cost

Dividend (if any)

From these variables, you can calculate the theoretical option price.

Implied volatility is the volatility implied by the option's price. These complex formulas cannot be factored for volatility. Because of this, one cannot input 5 pricing variables into a Closed Formula which then results in the implied volatility answer.

So the process of iteration is used. Starting with a volatility of zero, one incrementally increases the volatility by .01 . As the volatility input increases, the option price generated by the pricing formula increases. When this option price calculation equals the market price of the option, the volatility input used is the implied volatility.

The stock's IV is a Composite Volatility which is an evaluation of all of the options of a single security.

There are a variety of ways to calculate it. One well known author/service weights each individual option's implied volatility by its trading volume and its distance in or out-of-the-money. Another popular service calculates it by weighting delta and vega of each option.

The Composite Volatility number may vary somewhat from one method of calculation to another. That's not critical. The importance of the calculation is that the daily numbers can be assembled and volatility charts can be displayed in order to see how past daily implied volatilities compare to today's Composite Volatility.

As for your question of "How far in the future?", it is for the life of the option that you are looking at, aka expiration.