If VIX is the Implied Volatility of SPX, 30 days in the future, how many days into the future does VIX vol look?

Question

Question: if VIX is the Implied Volatility of SPX, 30 days in the future, how many days into the future does VIX vol look? +60 or +30?

Lets see if I'm on the right track:

• Premise 1: VIX is the Implied Volatility (IV) of SPX, looking +30 days into the future (actually, technically VIX is a variance swap, but for all intents and purposes its 99% correlated to the IV).
• Premise 2: Lets define VIX vol as the Implied Volatility (IV) of VIX, calculated from options on VIX, normalized to +30 days in the future (I am assuming that we calculate VIX vol using the same method as used to calculate SPX vol, by using the front and back month of the VIX options, then normalising this to a 30-day time horizon).
• Premise 3: Thus, VIX vol is equivalent to the vol-of-vol of SPX.
• Premise 4: VIX is the expected volatility of SPX, +30 days into the future.
• Premise 5: VIX vol is the expected volatility of VIX, +30 days further into the future.
• Premise 6: Therefore, VIX vol is the expected vol-of-vol of SPX, +60 days into the future?

Answer 1

You are very close. VIX vol is indeed a vol-of-vol. However the way VIX options actually work is that they expire into the futures, which themselves have value derived from 30-day options on expiration day.

That is to say, the VIX spot index today has no direct relationship to the VIX options you can trade today.

A VIX option vol is the volatility of (implied) volatility for a specific one month period starting on the contract expiration day, and ending a month after that.

Now, all this stuff is highly correlated of course, so you can pretend that VIX spot is telling you things about the options and vice versa. But the relationships need not hold solid, just as, say, eurodollar futures for disparate expirations can differ.