CBOE Volatility White Paper

Authoritative reference

Cboe Global Markets, Cboe Volatility Index — Methodology (current revision).

Primary PDF: https://cdn.cboe.com/resources/indices/Volatility_Index_Methodology_Cboe_Volatility_Index.pdf

The Cboe indices governance index lives at https://www.cboe.com/indices/.

Consumed by

Volatility — the CboeVix and Generalized windows compute the strip-integral variance per the methodology.

Formula

Variance per expiration is the CBOE strip integral:

σ^{2} = \frac{2}{T} \sum_{i} \frac{Δ K_{i}}{K_{i}^{2}} e^{r T} Q (K_{i}) - \frac{1}{T} {(\frac{F}{K_{0}} - 1)}^{2}

where:

$Q (K_{i})$ is the OTM-side mid-price at strike $K_{i}$ .
$K_{0}$ is the strike immediately below the forward $F$ .
$Δ K_{i} = (K_{i + 1} - K_{i - 1}) / 2$ for interior strikes; the endpoints take the single-sided width.
$T$ is the time-to-expiration in calendar years (calendar regime).

The index value is the square root of the time-weighted blend of the near-leg and next-leg variances, interpolated to the window's target term.

What the analytic implements

The CBOE strip integral (equation above).
The CBOE chain-selection rules under CboeVix: weekly SPXW + monthly SPX, third-Friday plus end-of-week.
Neumaier-compensated summation across the running variance accumulator (defends against the wide-grid precision pathology where deep-OTM contributions land below the running sum's ULP).
Replay-deterministic strike-grid prewarm via an upstream chain snapshot pinned to the subscribe-time (live) or historical timestamp (replay / historical via the replay scope::with_chain_snapshot).

What this site does not paste

The white paper's body is not reproduced here. The link above is the canonical reference; subsequent revisions of the methodology supersede both this page and the analytic's implementation as the document issuer publishes them.

CBOE Volatility White Paper ​

Authoritative reference ​

Consumed by ​

Formula ​

What the analytic implements ​

What this site does not paste ​