I have a couple questions about a stock's IV (Note: I am referring to future IV and not historical volatility): -- When someone states that a stock's IV is xx.x%, what are they referring to? Are they referring to the front week's options for that stock? The front month? Or, perhaps, the IV of options that are a certain distance away (30 days)? --If this is the case, how can one IV number refer to all the options for a given week or month? If a stock has 30 strikes for a given time period, is the IV for that time period the mathematical average for all strikes? Is the average weighted somehow with more import given to ATM options? Thank you in advance, Jay

"Implied Volatility" refers to the solution of the valuation formula using the price of an individual option and solving for volatility. Every option will usually have a slightly different implied volatility. When you see a reference to the implied volatility of an underlying it means some sort of averaging is being used. There is no standard way to calculate it and every permutation will produce a different number. If you are familiar with the VIX, for example, then you know it has been changed a few times over the years. If you want to understand the implied volatility being produced by a software package or other source then you need to find the formula being used and decide if it is valid for you.

"Implied volatility is expressed as a percentage of the stock price, indicating a one standard deviation move over the course of a year." Reference: http://www.optionsplaybook.com/options-introduction/what-is-volatility/

"Implied volatility is expressed as a percentage of the stock price, indicating a one standard deviation move over the course of a year." I would consider that the historical volatility of the underlying not implied volatility.

IV is calculated based on the price of an option. Therefore, when someone said IV is x%, he must say which strike he is referring to and not for an underlying. Unless he is referring to a weighted average IV like VIX. However, theoretically, IV should be the same for all strikes because IV refers to volatility of the underlying, and when we should have a single estimate of volatility for a given underlying regardless of strikes. But obviously we know from experience IVs aren't the same across strikes. The reason is the BS model is inaccurate. Before 1987, IVs were quite flat across strikes but after the crash, people realized BS model under forecasted the downside risks (for equities). As a result market bid up the lower strikes to cater to the higher risks. Hence the IV smile or the smirk. Therefore, before 1987, it would be okay to say IV is x% for a particular underlying, but after that one would have to specify which strike he's referring to. Here's a good read for those who wants to learn more about the vol skew http://www.emanuelderman.com/media/euronext-volatility_smile.pdf

Black-Scholes formula is indeed incorrect in the sense that it assumes stock prices are lognormally distributed, while it's easy to see that isn't so. But that could be fixed with a different model, except that it would also be incorrect for a more fundamental reason, which is that any option valuation formula would require us to know the future. The real BS of the BS model is that while we don't need to know the future price of the underlying to price an option, we do need to know the standard deviation of that future price. Which we don't. So in reality, an option price is formed in the marketplace by supply and demand, and volatility is not an input of the formula but rather an output. It varies across strikes because supply and demand vary. Below the money there is often demand from buyers of protective puts, so IV is higher. Above the money there is often supply from the sellers of calls, so IV is lower. The skew was flat before 1987 because people picking up pennies in front of the steamroller by selling puts haven't seen the steamroller yet. Now they'd rather pick up nickels. Coming back to the original question, of course there is no such thing as the implied volatility of a stock. The IV value for a stock displayed by various providers is some form of an index averaging individual option IVs to reduce them to a single value. How the index is computed is up to the provider, and different brokers will show you different values for the same stock. Right now TOS says AAPL IV is 28.03%, while IB says it's 24.85%.

Historical volatility looks backwards at what price has done in the past. Implied volatility is the expectation of future price movement. So when someone says that the IV of stock XYZ is 30% (without any other qualifying criteria), then this generally means that over the next year the stock has a future expectation of moving up or down by 30% from its current price.