"forward index price" in VIX calculation

[MK020]

Would it be more enlightening to clarify your objective?

F = strike + e^RT(call - put)

What does F represent in terms of a probability distribution? Does it represent the mode of expected prices?

VIX is NOT a good source for standard deviation as it relates to 30-day term AND includes impact of SKEW

I know that the actual probability distributions are skewed, but I thought VIX incorrectly assumed a normal distribution. No? Everything I read says it VIX gives annualized standard deviation in prices 30 days from now.

 

[stepandfetchit]

F is precisely defined, and is non-ambiguous:

Note this even shows the differing interest rates for each term. May be good to look closely at this to insure you understand what they do for the VIX calc. VIX calculation is not assuming anything related to a distribution... look again at the calculation. Seems like you want the tail to wag the dog. Using ATM_IV instead of VIX will provide a cleaner Volatility metric for the underlying. If you observe comparisons of VIX and the ATM IV (look at 30 day ATM IV to calibrate the comparison), you will notice VIX is always higher (near 24-30 delta away) due to how the value is calculated from the OTM strikes.

 

[MK020]

F is precisely defined, and is non-ambiguous

Yep, I get it. All there in black and white. But this is the final formula and doesn't show how everything was derived (what assumptions were made, etc). I'm trying to conceptualize the VIX.

I commonly see something along the lines of "VIX gives 1 standard deviation of expected prices in 30 days, so according to the VIX there's a 68% chance the price will fall within +/- (VIX/12) in 30 days". Those types of statements are only compatible with a normal distribution. You're saying they are incorrect interpretations?

 

[stepandfetchit]

Yep, I get it. All there in black and white. But this is the final formula and doesn't show how everything was derived (what assumptions were made, etc). I'm trying to conceptualize the VIX.

I commonly see something along the lines of "VIX gives 1 standard deviation of expected prices in 30 days, so according to the VIX there's a 68% chance the price will fall within +/- (VIX/12) in 30 days". Those types of statements are only compatible with a normal distribution. You're saying they are incorrect interpretations?

Ah! I am beginning to understand your query now! VIX is a "close enough for government work" type of approximation for that, but if you want a less tainted metric, use the ATM IV instead. I would not be surprised if Sosnoff may make similar statements, but if you watch him very much, you realize he typically plays very loose with details.
I used the VIX in the way you are a few years ago, and finally realized this was not the best metric available for that purpose.