# Volatility of Volatility A Volatility concept (Volatility estimators) in the LuxAlgo Library, with 1 indicator implementation. ## What is Volatility of Volatility? Volatility of volatility (vol-of-vol) is second-order volatility: a measure of how unstable the volatility series itself is. Compute a volatility measure first, such as [realized volatility](https://www.luxalgo.com/library/concept/realized-volatility/), ATR, or an implied index, then apply a dispersion calculation to that series rather than to price. Two markets can carry the same average volatility while one holds it steadily and the other lurches between calm and panic; vol-of-vol is the number that separates them. Options markets list the idea directly: VVIX measures the expected volatility of the VIX itself. High vol-of-vol means volatility estimates go stale quickly, which undermines anything calibrated to a trailing window: stop distances, position sizes, and band widths all inherit the instability. The concept has formal roots in derivatives pricing. Stochastic-volatility models, of which Heston's 1993 model is the standard reference, treat volatility as a random process with its own volatility parameter, and options desks have priced and hedged that parameter for decades. Cboe brought the idea to public screens with VVIX, which applies VIX-style methodology to VIX options. Technical traders borrowed it because the practical problem is identical at every scale: yesterday's volatility estimate is only useful if volatility is somewhat sticky. On a chart, vol-of-vol shows up as instability in everything volatility-driven: [ATR](https://www.luxalgo.com/library/concept/atr/) that lurches instead of drifting, [Bollinger Bands](https://www.luxalgo.com/library/concept/bollinger-bands/) whose [BandWidth](https://www.luxalgo.com/library/concept/bandwidth/) whips open and shut, and compression signals that fire and fail in quick succession. Measuring it directly, as a dispersion statistic on the volatility series, replaces that visual impression with a number that can be tracked, ranked against its own history, and used as a condition. ## How to measure volatility of volatility The measurement is a two-stage calculation: estimate volatility, then measure the estimate's instability. 1. Build the first-order series: rolling realized volatility, ATR, or an implied index if one exists for the market. 2. Convert to changes: work with period-to-period changes or log changes of the volatility series so its level does not dominate the statistic. 3. Apply a dispersion measure: a rolling standard deviation of those changes over a chosen window is the common choice. 4. Normalize for context: a [volatility percentile](https://www.luxalgo.com/library/concept/volatility-percentile-rank/) treatment of the result shows whether current instability is unusual for the instrument. 5. For US index volatility, compare with VVIX, the published implied measure of the VIX's own expected movement. ## How it's calculated Second-order volatility: a dispersion measure applied to a volatility series itself instead of to price. ``` r_t = ln(C_t / C_{t-1}) rbar_t = (1/n1) × Σ r_{t-i} over i = 0..n1-1 Vol_t = sqrt( (1/(n1-1)) × Σ (r_{t-i} - rbar_t)^2 over i = 0..n1-1 ) v_t = ln(Vol_t / Vol_{t-1}) vbar_t = (1/n2) × Σ v_{t-i} over i = 0..n2-1 VoV_t = sqrt( (1/(n2-1)) × Σ (v_{t-i} - vbar_t)^2 over i = 0..n2-1 ) C_t: close of bar t t: bar index i: bar offset inside a lookback window r_t: one-bar log return of price n1: first-stage volatility lookback (commonly 20 or 21) rbar_t: mean of r over the last n1 bars Vol_t: first-stage volatility, the sample standard deviation of returns over n1 bars v_t: one-bar log change of the volatility series n2: vol-of-vol lookback (commonly 20 to 60) vbar_t: mean of v over the last n2 bars VoV_t: volatility of volatility at bar t ``` Any volatility series can feed the second stage: realized volatility as above, ATR, or an implied index; simpler versions take the standard deviation of Vol itself rather than of its log changes. Multiply by sqrt(252) to annualize daily readings at either stage. VVIX is the listed, option-implied counterpart: the VIX methodology applied to options on VIX. ## How traders use it - As a stability check on risk inputs: rising vol-of-vol warns that volatility-targeted sizing and volatility-scaled stops are calibrated to a number that keeps moving. - As regime context: spikes in vol-of-vol often accompany transitions between calm and stressed conditions, so some regime models track it alongside the volatility level itself. - In options analysis: VVIX elevated relative to VIX flags expensive volatility convexity, which some traders read as hedging demand. - As a band-reading caveat: when vol-of-vol runs high, [Keltner Channel](https://www.luxalgo.com/library/concept/keltner-channels/) and Bollinger widths become moving targets, so traders lean on structure or add buffer rather than trusting freshly recalculated band distances. - As a squeeze filter: compression setups such as the [TTM Squeeze](https://www.luxalgo.com/library/concept/ttm-squeeze/) presume a stable quiet phase, and some traders discount squeeze signals that form while the volatility series itself is thrashing. ## Volatility of volatility vs first-order measures - **Realized Volatility** (https://www.luxalgo.com/library/concept/realized-volatility/): Realized volatility measures how much price moves; vol-of-vol measures how much that measurement moves. The first sizes risk, the second says how far the sizing can be trusted before it needs revisiting. - **Volatility Percentile/rank** (https://www.luxalgo.com/library/concept/volatility-percentile-rank/): Percentile locates today's volatility within its own history: it answers where the level sits, not how erratically it got there. A mid-percentile market can carry violent vol-of-vol during a regime transition, and the two readings together say more than either alone. - **BandWidth** (https://www.luxalgo.com/library/concept/bandwidth/): BandWidth is a chart proxy for the volatility level. The choppiness of the BandWidth line itself is an informal vol-of-vol read, which a dispersion calculation on the volatility series makes explicit and comparable over time. ## FAQ ### How do you measure volatility of volatility? Build a volatility series first, such as rolling realized volatility, ATR, or an implied-volatility index, then measure that series' own variability, typically as a rolling standard deviation of its changes or log changes. For index options there is a listed version: VVIX, which applies the VIX methodology to options on the VIX itself. ### Why does volatility of volatility matter for traders? Because most risk plumbing assumes the current volatility estimate stays representative: ATR stops, volatility-targeted position sizes, and band widths are all trailing calibrations. When vol-of-vol is high that assumption fails, and the number you sized with can be badly wrong within days. Stable-volatility regimes forgive imprecise inputs; unstable ones punish them. ### Is VVIX the same thing as volatility of volatility? VVIX is one listed, implied instance: the expected 30-day volatility of the VIX, derived from VIX option prices. Vol-of-vol in general applies to any volatility series, realized or implied, on any instrument. VVIX is to vol-of-vol roughly what the VIX is to volatility: a specific benchmark, not the whole concept. ### Does high volatility imply high volatility of volatility? They are often correlated but are not the same thing. A market can be persistently and stably volatile, with wide but predictable ranges, while another is quiet on average yet prone to abrupt shifts. Vol-of-vol spikes are most associated with transitions between regimes rather than with the level of volatility itself. ### How can I see volatility of volatility on an ordinary chart platform? Most platforms allow indicators on indicators: apply a standard deviation or rate-of-change study to an ATR or realized-volatility series and you have a workable vol-of-vol proxy. Watching how erratically BandWidth moves gives a rough visual version, and community scripts exist that score exactly this. ### What window should the calculation use? There is no standard. The first-stage window defines what counts as volatility, and the second-stage window defines how far back instability is judged. Shorter second-stage windows catch regime breaks faster at the cost of noise. Consistency matters more than the specific choice, and percentile-ranking the output softens the dependence on any single setting. ## Implementations in the Library - Volatility of Volatility (LuxAlgo): https://www.luxalgo.com/library/indicator/volatility-of-volatility/ ## Related concepts - Volatility Estimators: https://www.luxalgo.com/library/concept/volatility-estimators/ - Close-to-close Historical Volatility: https://www.luxalgo.com/library/concept/close-to-close-historical-volatility/ - EWMA Volatility: https://www.luxalgo.com/library/concept/ewma-volatility/ - Parkinson Estimator: https://www.luxalgo.com/library/concept/parkinson-estimator/ - Garman-Klass Estimator: https://www.luxalgo.com/library/concept/garman-klass-estimator/ - Rogers-Satchell Estimator: https://www.luxalgo.com/library/concept/rogers-satchell-estimator/ - Yang-Zhang Estimator: https://www.luxalgo.com/library/concept/yang-zhang-estimator/ - Garman-Klass–Yang-Zhang Hybrid: https://www.luxalgo.com/library/concept/garman-klass-yang-zhang-hybrid/ - Jump Detection: https://www.luxalgo.com/library/concept/jump-detection/ - Volatility Signature Plot: https://www.luxalgo.com/library/concept/volatility-signature-plot/ --- Source: https://www.luxalgo.com/library/concept/volatility-of-volatility/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/