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How VIX Option Volatility Maps to Forward Volatility Periods

Article Quant Q&A · Author: Contango
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Summary

The note clarifies what volatility implied by VIX options represents. VIX itself reflects an estimate of S&P 500 volatility over a forward 30-day period, but a VIX option does not simply measure the future volatility of today’s spot VIX. VIX options expire into VIX futures, whose value is tied to the volatility index calculated on the option’s expiration date.

As a result, the option’s implied volatility describes uncertainty in the VIX futures level over the option’s life. Interpreted in terms of the underlying equity volatility, it relates to the volatility of a later one-month volatility period that begins at option expiration. The proposed “60 days ahead” intuition is therefore approximate, not an exact universal mapping. Spot VIX and VIX options are often correlated, but their relationship can vary across maturities, so timing and instrument distinctions matter when interpreting or trading them.

Key ideas

  • VIX option implied volatility is a measure of volatility in the relevant VIX futures contract.
  • VIX options expire into futures rather than directly into today’s spot VIX.
  • The futures value at expiration reflects a subsequent 30-day S&P 500 volatility period.
  • Spot VIX and VIX option prices may be related, but the relationship can vary by maturity.

Tags

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


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












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 by Brian B (score 6, accepted)

https://quant.stackexchange.com/a/1991

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.