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Constructing the CBOE 9-Day Volatility Index from SPX Options

Article Quant Q&A · Author: bruno
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Summary

The document explains that VIX9D applies the VIX methodology to S&P 500 options whose expirations bracket a nine-day horizon. The calculation uses two option maturities, derives implied volatility for each using the standard VIX procedure, and interpolates between them to estimate volatility at the target horizon. The example selects an earlier and a later expiration around the nine-day point, illustrating how the maturity bracketing works.

A separate comment highlights a measurement issue when comparing implied and realized volatility: VIX-family indexes use calendar days, while the project’s realized volatility estimate uses trading-day closing returns. That difference can complicate comparisons. The discussion does not reproduce the full VIX calculation or provide empirical validation; it points to the VIX white paper as the source for implementation details.

Key ideas

  • VIX9D adapts the VIX calculation to options expiring around a nine-day horizon.
  • The calculation uses near-term and next-term SPX options that bracket the target maturity.
  • Implied volatility from each selected maturity is interpolated to the nine-day point.
  • Calendar-day horizons in volatility indexes can complicate comparisons with realized volatility measured from trading-day returns.

Tags

OptionsVolatilityDerivatives pricingUS markets
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# CBOE VINXE or VIX9D Index Construction


# CBOE VINXE or VIX9D Index Construction












I have not been able to find a White Paper on how the CBOE VIXNE index is constructed. Any lead to short term volatility index calculations would be appreciated. Thanks

## Answer by Martin Georg Haas (score 4, accepted)

https://quant.stackexchange.com/a/58477

As stated on the VIX9D page (see the link from noob2):

> The CBOE S&P 500 9-Day Volatility Index SM (VIX9D) estimates the expected 9-day volatility of S&P 500® stock returns. Similar to VIX®, VIX9D is derived by applying the VIX algorithm to options on the Standard &Poor's 500 Index (SPX options), but it uses SPX options with expiration dates that bracket a nine-day period of time.

This means that for VIX9D, you can exactly follow the VIX Whitepaper, but simply use contracts with a different maturity.

E.g. for today (05.10.2020), the 9-Day maturity would be on the 14th. We then select the "near-term" contract from the 9th (= 4-day maturity) and the "next-term" contract from the 16th (= 11-day maturity), calculate their respective implied volatility as described in the Whitepaper and interpolate the 9-day value of the VIX, which lies in between these contracts.

## Answer by Felix Fujishiro (score 1)

https://quant.stackexchange.com/a/58566

Martin, I believe this is your research paper that you mentioned? https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3644295

For my time-series class at DePaul, I chose for my group project to study the relationships between the SPX, VIX, VIX9D, VIX3M, etc. One of the things we're wrestling with is trying to match the realized volatility of the SPX with the various VIX indices, because we're calculating the former from the log returns of the closing prices on the trading days, whereaas the latter are based on calendar days. If you would not mind, could I also contact you regarding the VIX calculation algorithm?

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