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I know that each individual option has it's own implied volatility, but how do you go about calculating the overall implied volatility for an underlying?

For example when someone sais the IV of a certain underlying is 40%, they are not referring to a specific option/strike. They mean that the option market as a whole is implying a volatility of 40%. How is that 40% calculated? Im guessing it is something along the lines of calculating the IV for every option available and taking some sort of average?

Secondly, how do you go about calculating the historical IV over a given time period. For example in most options trading platforms (eg: TWS, ThinkOrSwim, etc) you can pull up a chart of a specific underlying along with it's IV over a given time period. How would you go about recreating that?

Again I presume you do something like:

One day at a time, get the closing price for every active option
Calculate the IV for all the options at every strike
Perform some sort of average
Move to the next day

It seems impractical to calculate the IV of every single active option. Is it perhaps only done using the front month? (and if so, does that include weeklies and monthlies?). However this also doesn't seem right because IV is an implication of the next years worth of volatility,...so why would only the front month options be used?

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Are you able to look at the code for that indicator?
I would be pretty sure they aren't calculating a volatility index like the vix on each underlying. That would be awesome.
Of course it doesn't make sense to talk about IV on the stock itself as IV is something solved for in an options pricing formula.
it probably is something simple and less useful like just plotting the next expiration ATM call IV.

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The term historical or realized volatility refers to the movement of the underlying asset. Implied volatility is specific to individual options but an average can be created using combinations of options, as for example, the VIX.

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Have you seen tastytrade.com? Try doing a search there for those terms. They have a lot of segments on volatility for both the layman and mathematicians. For the math part there is "The Skinny on Options Math":

Thanks for this. However I somehow doubt that the IV number im referring to is calculated by determining a VIX for every underlying. But if anyone else could expand on this that would be great.

This is what I was thinking (and hoping). Something like calculating an average (weighted average?) for each expiration's IV. I just can't seem to get a definitive answer anywhere.

Correct. Historical volatility refers to the underlying. IV refers to specific options and implies the expected 1SD volatility over the coming year.

Neither of those figures are what im trying to calculate. The figures im trying to calculate are highlighted in the screenshots attached in the first post.

Thanks, I watch tastytrade regularly. Unfortunately I haven't found anything that actually answers my question. Everything that is discussed on tastytrade (and everywhere else) is always referring to either the historical volatility of the underlying or the IV of a specific option, or the IVRank. None of these are what im trying to determine. I may actually shoot tt an email to ask about this.

I've attached screenshots in my original post to show which IV number im trying to calculate. That IV number is not derived from an individual option.

Thanks for everyones replies. I have asked this question in several places on the interwebs and no one has been able to answer.

Im hoping @SMCJB chimes in if he gets a chance as I believe he has some knowledge in this area?

Just wanted to post another screenshot, this time from TWS. Each option (put and call) has it's own IV. However what im trying to find out is, how is the IV in the top section calculated? My simplistic (non-mathematical) mind sais it's some sort of average based on all the individual options. But that is probably wrong.

As you are all probably aware most option pricing models have an underlying assumption that the prices returns of the underlying asset are log normally distributed. You are also probably aware that this is not statistically correct and that the real distributions have 'fatter tails' than would be expected. Hence very low probability occurrences actually happen a lot more frequently than they should. Option models handle the 'fat tail' phenomenon by using the concept of skew, saying that OTM options have higher IVs. But that's not technically correct. The underlying asset is the same no matter what strike option we are looking at, there is no "single" implied volatility of an underlying asset, There is though one probability density function ("PDF") of expected outcomes for the underlying. That PDF can be calculated by using the implied volatility of each strike, but that it's above my pay grade and involves so pretty heavy math. It would be nice if there was an easy way to know what the Kurtiosis & Skew of each underlying asset would be and to use/chart that as an indicator.

Thanks for this. Unfortunately this is also probably way above my math skills (which are laughable at best). But I will certainly have a skim through these pdf's. Thank you.

So for anyone else that's interested, it turns out that @ElChacal is 100% correct. I contacted TastyTrade and their research department replied indicating that the above pdf is what is used to calculate the 'single' IV figure in both ThinkOrSwim and Dough. Seeing As TT developed Dough and have a tight relationship with TOS,...I figure they are correct.

So basically, for every single underlying, a vix calculation is performed which is a weighted average over several expirations and multiple strikes.

Diversification is the only free lunch

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