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Extending the VIX Method to Longer-Dated Implied Volatility

Article Quant Q&A · Author: Chuck Remes
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Summary

The document considers adapting the CBOE VIX calculation to estimate SPX implied volatility over a 60-day horizon. The proposed changes are to select option expirations centered around that target horizon, rather than the standard VIX window, and to use the number of minutes in 60 days in the annualization step. The question also suggests applying the same approach to still longer horizons.

The brief accepted response says the approach is broadly on track and points to CBOE’s three-month volatility index methodology as a reference. It does not provide a derivation or validate every proposed adjustment. The note therefore highlights the key idea of matching option maturities and time scaling to the desired horizon, while leaving implementation details, such as precise maturity selection and interpolation, to the referenced index methodology. The discussion concerns an implied-volatility index calculation, not a forecast of realized volatility.

Key ideas

  • A longer-horizon volatility index requires option expirations suited to that horizon.
  • The time scaling in the index formula must reflect the target maturity.
  • The response recommends consulting the methodology for CBOE’s three-month volatility index.
  • The document does not derive the complete calculation or discuss its empirical performance.

Tags

OptionsVolatilityDerivatives pricing
Full text
# If VIX measures SPX IV 30-days in future, how to modify formula to calc IV 60-days in future?


# If VIX measures SPX IV 30-days in future, how to modify formula to calc IV 60-days in future?












So I've gone over the CBOE VIX white paper a few times and understand it well enough to have written (Ruby) code to produce the correct VIX. I have the older version of the paper where it only used standard/monthly options to produce the number (published in 2009) and I also have the most recent paper published in 2014 that modified the rules to use weekly options. I understand the differences and why they updated their rules.

Here's the white paper: http://www.cboe.com/micro/vix/vixwhite.pdf

Now I want to calculate the 60-day VIX. Please confirm that I'm on the correct path in modifying the rules and the formula.

- Instead of picking options that expire between 23 and 37 days out, I'd want to grab the series that expire between 53 and 67 days out.

- In Step 3 of the formula (as listed in the white paper), use number of minutes in 60-days for N(60).

As a consequence of 2, we are weighting to a 60-day timeframe. To do a 90, 120, 150, or 180-day VIX I would make similar changes as above.

Does this make sense or have I made a fundamental error?

## Answer by pyCthon (score 1, accepted)

https://quant.stackexchange.com/a/25903

Your on the right track. See the link here for how the CBOE VXV - 3 month volatility index is calculated.

http://www.cboe.com/micro/vxv/3monthvix.pdf

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.