How to calculate daily Implied Volatility?

S

Sure Chap

I need help calculating the implied volatility of a stock/index for a single day. I referenced the site: https://www.optionsanimal.com/using-implied-volatility-determine-expected-range-stock/
Formula: (Stock price) x (Annualized Implied Volatility) x (Square Root of [days to expiration / 365]) = 1 standard deviation.

Here's my attempt, I didn't want to use the IV of a option set to expire a year out because I wanted to be as accurate as possible. So I chose the IV of a weekly option, in this case 6 days left to expiration with the IV of 15.51%.

Current S&P 500 Index: ~2005
Implied Volatility: 15.51%

To calculate the daily IV is the formula:

Standard Deviation = 2005 x 0.1551 x sqrt(1/252)
Daily IV = .97% = Standard Deviation/Current Price?


or

Standard Deviation = 2005 x 0.1551 x sqrt(1/365)
Daily IV = .81% = Standard Deviation/Current Price?


some places are saying there's 252 trading days, but I thought the IV was based on every day of the year including non-trading days.

So confused here...
 
rmorse said:
It is based on actual trading days, because on non-trading days stocks can't move. 252 works.
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Hi Rmosre, thanks for the help again; but does it matter if I use the IV of a weekly or a yearly option? There's about a few percentage point difference, for example the S&P 500 call option with strike price 2000, the weekly(6 days) is 15.62% vs the yearly(363 days) is 16.07%
 
Not sure. I've never been one for exactness. I always used an estimate of 16 as 1% daily moves. What do you want to use the results for? If it is for a learning process, estimates are fine. If you were building a market making program or volatility trading algo, you will need to be more accurate especially for options on higher priced symbols where each fraction of a point means something.
 
Last edited:
a few notes:


"... because I wanted to be as accurate as possible ... "
Then why not use the CBOE method (https://www.cboe.com/micro/vix/vixwhite.pdf) which is also partially used by TOS (they claim they do, I have not computed myself to confirm) for each Expiry. Note: for the 6DTE series, the IV would be 18.76%, not 15.51%. I'd think using Monthlies would provide more accurate info (due to more liquidity), and the 30DTE (or VIX) may be the most accurate (or at least you can compute it). One issue you will have with your approach is you will typically assume "contango" pricing with a smooth DTE curve. This is not always the case.
Regarding 252 VS 365 ; I share your discomfort in the "wishy washy" use. I think I just picked the 252 for all my stuff to be consistent, but it likely is not a major factor, if you are consistent.
 
rmorse said:
Not sure. I've never been one for exactness. I always used an estimate of 16 as 1% daily moves. What do you want to use the results for? If it is for a learning process, estimates are fine. If you were building a market making program or volatility trading algo, you will need to be more accurate especially for options on higher priced symbols where each fraction of a point means something.
More...

Part strategy building, part learning. I think I'm overthinking this, I wanted to find the implied volatility of a stock daily so I can find a good stop loss point. I just opened up my thinkorswim platform and I'm literally overwhelmed by the indicators available. I think what I was looking for might be related to one of those standard deviation indicators.

I truly, appreciate the help Rmorse. Volatility indicators are a lot easier than manually calculating the daily implied volatility.
 
stepandfetchit said:
a few notes:


"... because I wanted to be as accurate as possible ... "
Then why not use the CBOE method (https://www.cboe.com/micro/vix/vixwhite.pdf) which is also partially used by TOS (they claim they do, I have not computed myself to confirm) for each Expiry. Note: for the 6DTE series, the IV would be 18.76%, not 15.51%. I'd think using Monthlies would provide more accurate info (due to more liquidity), and the 30DTE (or VIX) may be the most accurate (or at least you can compute it). One issue you will have with your approach is you will typically assume "contango" pricing with a smooth DTE curve. This is not always the case.
Regarding 252 VS 365 ; I share your discomfort in the "wishy washy" use. I think I just picked the 252 for all my stuff to be consistent, but it likely is not a major factor, if you are consistent.
More...
Thanks for the input Stepandfetchit, the math and indicators are all getting to me. Need a little time to let it all sink in. I'm actually surprised the depth of math involved here, as a former engineer even I'm getting confused. I think I have what I'm looking for, a volatility indicator.
 
Sure Chap said:
I need help calculating the implied volatility of a stock/index for a single day. I referenced the site: https://www.optionsanimal.com/using-implied-volatility-determine-expected-range-stock/
Formula: (Stock price) x (Annualized Implied Volatility) x (Square Root of [days to expiration / 365]) = 1 standard deviation.

Here's my attempt, I didn't want to use the IV of a option set to expire a year out because I wanted to be as accurate as possible. So I chose the IV of a weekly option, in this case 6 days left to expiration with the IV of 15.51%.

Current S&P 500 Index: ~2005
Implied Volatility: 15.51%

To calculate the daily IV is the formula:

Standard Deviation = 2005 x 0.1551 x sqrt(1/252)
Daily IV = .97% = Standard Deviation/Current Price?


or

Standard Deviation = 2005 x 0.1551 x sqrt(1/365)
Daily IV = .81% = Standard Deviation/Current Price?


some places are saying there's 252 trading days, but I thought the IV was based on every day of the year including non-trading days.

So confused here...
More...

This is what I use with my trusty HP 17bII+

Screen Shot 2015-12-19 at 12.26.53 PM.png
 
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