"forward index price" in VIX calculation

Hi everyone, I was reading the VIX whitepaper published by CBOE (https://www.cboe.com/micro/vix/vixwhite.pdf) and wondering what the interpretation of the "forward index price" (F) is in this context.

If I were to model the possible values of SPX with a normal distribution, I would use VIX as my standard deviation, but what would be the center of the distribution? Would it be the current price of the index, or would I use this "forward index price"?

 

Forward can be imputed directly from options:

Code:

 F = call(k0) - put(k0) + k0 

and k0 is the strike where abs(call - put) is the smallest

Forward is the correct center of the distribution, since it takes into account funding and dividends.

 

Thanks. I noticed from the VIX whitepaper that they use the bid-ask midpoint for call and put prices. But when I do the calculation for some historical EOD data, I sometimes get a value for F that is larger than the current index price at the time. That doesn't make sense to me. Is there something wrong with my data? How could F be larger than current price? I thought it would only be lower because of dividends.

 

For a while (a few months) a year or so back, I was independently calculating the VIX values from SPX options by following the algo in their white paper. This can produce values that are very "close" to the published VIX numbers, but to get exact match one would need to replicate the data samples precisely, which they do no publish the precise sample times they take the data from. Should not really matter, unless you are trying to exactly duplicate the values. Note: the VIX values will appear "noisy" due to the exhaustion of sequential strike distances with no zero BIDs.
If you are looking for more precision, you may want to consider using ATM IV instead of the VIX, which will remove the impact of SKEW, and allow more precise term correlation. (My 2 cents)

 

Depending on when that was, it could have been interest rates.

 

Unless I'm doing something wrong, I actually see it happen often, even today.
https://www.barchart.com/stocks/quotes/$SPX/options

The SPX closed at 2488.65. For options expiring 4/6/2020, the 2490 strike currently has the smallest difference between Call and Put:

CALL 2490 midpoint = 32.95
PUT 2490 midpoint = 31.65

F = (32.95 - 31.65) + 2490 = 2491.30

 

Are your options snapped at the cash close (16:00) or at futures settlement (16:15)?

 

For the barchart website, I'm not 100% sure. But for the data on my hard drive, it's snapped at 16:00.

 

On further examination, even though the data is advertised as being all from 16:00, I'm suspecting that is not the case. Some of the prices just don't make sense given the "current price" of the index.

 

Your objective is not clear! Your original post expressed clarity on the CBOE VIX white paper reference to F, but your last post relates to the 6APR term.
Seems you are mixing apples and oranges inappropriately.
Your first post seems to suggest you have a flaw in your reasoning... you seem to imply VIX should be relevant to expirations other than 30 days. VIX is NOT a good source for standard deviation as it relates to 30-day term AND includes impact of SKEW. Would it be more enlightening to clarify your objective?