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?

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.

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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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@DarkPoolTrading this is a great question.
Basically, my initial intention was to check if I could come up with different VIX's for any instrument. The formula is a bit of a hiccup but no rocket science.
Since I don't know anything about options and have not traded them, the issue I have is finding a "Ticker" for the "Near term and Next Term strike prices" or the rest of the inputs in the equation and plot them in Ninjatrader for instance. Of course, in an automated way, I wouldn't wish to check what bid and ask prices are and write them in excel every single time.

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Well I haven't come up with anything yet, I just had the intention but I am not sure how to fill in the blanks/inputs (in an automatic way) for the formula.

Sorry ElChacal, I meant from TOS.
Trying to do it in Ninja I think is going to be such a headache data wise. I don't think there is much in the way of historic options data on retail data feeds.
You will probably have to store your own data and will not have the ability to back fill. I am sure it would be a great learning experience to calculate though.

If you know the option price, strike & underlying price, one can calculate historical Implied Volatility using Black-Scholes formula. This would require little programming in Python using Vollib quant library.

IV of an underlying stock can be roughly calculated using weighted average of IV of ATM & 2 near strike OTM put & call options.

that's no vix, there are two ways that one can come up with an iv for an underlying and 3 ways you can have the historical iv

1. for the underlying the simplest method is to use the atm IV including the moneyness relationship, for instance if your underlying is 18 to 18.24 you use the 18 strike iv as an itm, if it goes over 18,26 you use 18,50 as atm in the middle take into account the direction is coming the underlying from above or below. So if today is 18,24 you use 18 as atm for iv, tomorrow is 18,6 you use 18,50 BUT the values for yesterday will be kept as for 18. Thats the easy way that goes for a long time

2. you can take a more complex process that will weight the IV off al strikes, to to this you have 3 ways.
1. Actual contract volume weight,
2. open interest weight
3. a combination of 1 and 2
4 I have been experimenting of a combination of 1.2, and moneyness relationship

3 way is the iv calculation for each day for each exercise but is not the case you mention, this method will give an historical IV for each contract, regarding you use the method of absolute exercise price or you use the moneyness relationship (in this last case the atm one is the same as the first example I gave)

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Technically, implied volatility is only applicable for options. Implied volatility is a function of an option's price and is backed out from the price. Based on the option chain, you can see that each strike will likely have a different implied volatility based on the volatility skew / volatility smirk.

If you want to arrive at a single volatility number for the underlying, you would have to calculate a form of weighted average of the different implied volatilities of the option chain. For instance, the current VIX calculation uses a formula to derive expected volatility by averaging the weighted prices of out-of-the-money puts and calls.

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VIX is interpreted as annualized implied volatility of a hypothetical option on S&P500 with 30 days to expiration, based on the prices of near-term S&P500 options traded on CBOE.

Contrary to what many people believe, the VIX is NOT calculated using Black-Scholes or any other option pricing model. There is a formula which directly derives variance from the whole set of prices of options with the same time to expiration. Two different variances for two different times to expiration are then interpolated or extrapolated to get 30-day variance. This variance is then transformed into standard deviation (by taking the square root) and multiplied by 100.

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Can you demonstrate an example of the calculation? Without a math background, it's hard for me to visualize how to implement some of the steps, like #2

Well in order to do this I understand one would need historical data of options... The only source I've seen is CBOE but it is very pricy for a given set of years. https://datashop.cboe.com/

Even if you get past the data issue I am not sure on which platform you could backtest this data (for instance Ninja only has price and volume data...). I'd like to backtest it in a multi-instrument strategy which makes it even a bit harder. If anyone has input on this or has tried it before it would be very much appreciated.

There are VIXes for all the mega assets, such as Apple. Each strike has its own volatility, too.

While you are at it, you might want to explore the concept of future volatility, such as expressed by VIX futures.

You might want to get a subscription to LiveVol Core. It's not that expensive and offers probably all the functionality you need as for volatility. You can get it for free with certain brokers.

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