What is the VVIX?

By EC Assets Research Team, Volatility & Derivatives Desk · Published · Updated

VVIX — The volatility of the VIX itself. Calculated from VIX options using the same variance-swap methodology as VIX, it summarizes the market's expected 30-day volatility of the volatility index in annualized percentage points.

What the VVIX Actually Measures

VVIX is the volatility of the VIX. Calculated by the CBOE using the same variance-swap methodology as the VIX itself but applied to options on the VIX rather than options on the SPX, it expresses the market's expected 30-day volatility of the volatility index as an annualized standard deviation in percentage points.

VVIX answers a different question than VIX. VIX prices the next 30 days of SPX variance. VVIX prices the next 30 days of variance in VIX. Where VIX is commonly called the fear gauge, VVIX is the fear-of-fear gauge, reflecting what market participants pay to hedge the volatility of their hedges. The two indices interact, but neither is reducible to the other.

How It Works

VVIX uses the model-free variance-swap replication identity, the same construction CBOE adopted for the modern VIX in 2003:

$$\text{VVIX}^2 = \frac{2}{T} \sum_i \frac{\Delta K_i}{K_i^2} e^{rT} Q(K_i) - \frac{1}{T}\left(\frac{F}{K_0} - 1\right)^2$$

where $T$ is time to expiration, $K_i$ runs over the strikes of VIX options, $Q(K_i)$ is the midpoint of bid-ask for the appropriate out-of-the-money option (call above forward, put below), $F$ is the VIX forward, and $K_0$ is the strike immediately below $F$.

The calculation interpolates between two expiries to produce a constant 30-day measure. The output is then scaled to annualized volatility points, the same units as VIX, but expressing VIX's expected percentage standard deviation rather than SPX's.

Because the inputs are VIX options, VVIX inherits the shape of the VIX volatility surface. VIX call skew is structurally positive: VIX is bounded below at zero and effectively unbounded above, so out-of-the-money VIX calls trade rich relative to puts. This wing-call dominance lifts VVIX above the at-the-money implied volatility of VIX options.

Worked Example

Suppose the following:

Apply the Rule of 16 to VVIX (treating it as an annualized volatility):

$$\sigma_{\text{VIX, daily}} \approx \frac{90}{16} = 5.6%$$

The expected one-day move in VIX, as a percentage of its current level, is 5.6 percent. In absolute VIX points:

$$\Delta\text{VIX}_{1\sigma} \approx 18 \cdot 0.056 \approx 1.0 \text{ VIX point}$$

A typical day, at these levels, sees VIX move between roughly 17 and 19. Two standard deviations covers 16 to 20.

VIX level VVIX Daily 1σ VIX move (%) Daily 1σ VIX move (points)
12 75 4.7% 0.56
16 85 5.3% 0.85
20 95 5.9% 1.18
30 120 7.5% 2.25
50 160 10.0% 5.00
80 200 12.5% 10.00

Source: Indicative levels; actual VVIX values depend on the full VIX option surface.

VIX has spiked above 80 during major crises; VVIX has spiked above 200 in the same windows. The amplification reflects vol-of-vol convexity: large VIX moves themselves move violently when realized.

When It Applies (and Limitations)

Liquidity in VIX option wings

VIX options have less depth than SPX options, particularly in long-dated strikes and far-out-of-the-money wings. The VVIX calculation aggregates wing options whose quotes can be wide and indicative rather than transactable. In stressed markets, VVIX may move on quote artifacts rather than transactions, producing readings that overstate or understate true vol-of-vol.

Single-underlying dependency

VVIX is calculated only on VIX options. Volatility-of-volatility for other underlyings (NDX, FTSE, single-name equities) is calculable in principle but is not produced as a standard benchmark. Cross-asset vol-of-vol comparisons require ad-hoc calculations.

Asymmetric distribution

VIX is bounded below at zero and effectively unbounded above. Its distribution is highly right-skewed and approximately lognormal. VVIX uses a symmetric variance-swap construction that approximates lognormal vol-of-vol but does not capture the asymmetry exactly. For extreme moves, the approximation introduces measurable error.

Relationship to VIX is regime-dependent

In calm markets, VIX and VVIX often move together, both at the low end of their ranges. In transitions to stress, VVIX typically leads, rising before VIX spikes materialize. In peak crisis, VIX rises faster than VVIX, compressing the ratio. The two measures' relationship is not stable across regimes and cannot be summarized in a single coefficient.

Term structure

The published VVIX is a 30-day measure. The VIX option surface includes expiries from one week to nine months, each producing a different vol-of-vol value. A 30-day point estimate hides term-structure information that some practitioners track separately by computing VVIX at multiple horizons.

Sample-size considerations

VVIX has been published since 2012, a sample that includes the 2015 China devaluation, the 2018 Volmageddon, and the 2020 pandemic shock but excludes the 2008 crisis. Long-sample statistics for VVIX are necessarily shorter than for VIX and are dominated by a small number of regime events.

Why It Matters for Institutional Investors

Tail-hedge pricing

The cost of a VIX call option, used as an explicit tail hedge, depends on its implied volatility, which is summarized in VVIX. A high VVIX raises the cost of tail-hedge programs that buy upside VIX calls; a low VVIX makes the same hedges cheaper. Tail-hedge timing is influenced by VVIX levels, with many programs structurally biased toward accumulating hedges when vol-of-vol is depressed.

Vol-of-vol exposure

Variance swap sellers carry short vol-of-vol exposure through the convexity of the variance swap payoff. A rising VVIX increases the marked value of long-volga positions and weighs on short-volga positions, often without much change in spot vol. Volga management is a distinct discipline within volatility trading and uses VVIX as one of its primary inputs.

Signaling

Persistent elevation in VVIX without a corresponding move in VIX signals that market participants are paying up for protection against future volatility spikes. Allocators read this as a forward-looking stress indicator distinct from realized or current implied volatility. Some systematic frameworks include the VVIX-to-VIX ratio as a regime-classification input.

Volatility surface fitting

VVIX provides one observable summary of the level of the VIX option surface. Models that fit the SPX surface jointly with the VIX surface, sometimes called consistent stochastic-vol or affine vol-of-vol calibrations, use VVIX as one of their calibration targets. The consistency constraint between the two surfaces is non-trivial and remains an active area of derivatives research.

Convexity products

Convex volatility products (VIX call spreads, VIX ratio spreads, vol-of-vol swaps where they trade) price directly from VIX option implied volatilities. The VVIX level enters their cost and hedging dynamics, and changes in VVIX move their mark even when VIX itself is flat. Desks running structured vol-of-vol books monitor VVIX continuously alongside VIX.

Risk reporting

Funds with material options exposure typically report two vol-related risk numbers: a vega number (sensitivity to a one-point change in VIX or ATM implied vol) and a vega-of-vega or volga number (sensitivity to a change in VVIX). The two numbers can move independently, and reporting only the first hides exposure that VVIX captures.

References

  1. Sinclair, E. (2013). Volatility Trading (2nd ed.). Wiley.
  2. Natenberg, S. (2015). Option Volatility and Pricing (2nd ed.). McGraw-Hill.
  3. Cboe. VIX White Paper: The Cboe Volatility Index. (https://www.cboe.com/vix)

Frequently asked questions

Is VVIX higher or lower than VIX on average?

VVIX is structurally higher than VIX because vol-of-vol on a positively-skewed underlying (VIX itself) is amplified by the convexity of the variance-swap calculation. Long-sample averages place VVIX near 90, while VIX averages near 19.

Why is VVIX typically above 80?

VVIX inherits the call skew of VIX options. Because VIX is bounded below at zero and unbounded above, out-of-the-money VIX calls trade rich relative to puts. The variance-swap construction weights these calls heavily, lifting VVIX above the at-the-money level.

Can VVIX move when VIX is unchanged?

Yes. VVIX summarizes the entire VIX option surface, particularly the wings. Shifts in demand for upside VIX calls or downside VIX puts can move VVIX significantly even when the at-the-money VIX option implied volatility (and therefore VIX itself) is stable.

How does VVIX relate to tail-hedge pricing?

Tail-hedge programs that buy out-of-the-money VIX calls pay implied volatilities reflected in VVIX. A higher VVIX directly raises hedge costs; a lower VVIX makes accumulation cheaper. Many systematic programs accumulate hedges preferentially when VVIX is depressed.

Is there a Rule of 16 equivalent for VVIX?

Yes. The same daily-conversion logic applies: VVIX divided by 16 gives the expected daily one-sigma percentage move in VIX itself. A VVIX of 96 corresponds to roughly a 6 percent daily move in VIX, large in percentage terms but often small in absolute points when VIX is low.

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