What is Volatility of Volatility (VVIX)? Definition, Formula, and Example
Volatility of volatility (VVIX) measures the expected volatility of the CBOE Volatility Index (VIX) using the variance swap methodology applied to VIX options.
What is Volatility of Volatility?
Volatility of volatility, tracked by the CBOE Volatility of Volatility Index (VVIX), measures the expected 30-day volatility of the VIX index. It is derived from the prices of VIX options using a variance swap formula. While the VIX measures the implied volatility of the S&P 500 (SPX), the VVIX measures the implied volatility of the VIX itself. A high VVIX indicates that traders expect violent swings in volatility, which correlates with market stress and aggressive hedging activity. A low VVIX indicates stable volatility expectations and a quiet market regime.
How VVIX is Calculated
The VVIX is calculated using the same variance swap methodology used for the VIX, but applied to VIX option prices instead of SPX options. The formula uses out-of-the-money VIX calls and puts across a wide range of strikes. The variance swap rate is calculated as:
Volatility = √(2/T) × Σ(ΔK/K²) × e^(RT) × Mid(K)
Where T is the time to expiration, K is the strike price, and Mid(K) is the mid-price of the VIX option at strike K. The VVIX aggregates two near-term expirations to create a constant 30-day expected volatility of the VIX. Because the VIX is already a mean-reverting, negatively skewed asset, VIX options exhibit extreme skew—calls are heavily bid up compared to puts. The VVIX captures this skew and the rapid repricing of volatility expectations.
Worked Example
On August 5, 2024, a global carry trade unwind triggered a massive market selloff. The VIX spiked from 18 to over 65 intraday. Leading up to and during this event, the VVIX surged from 90 to over 170. Traders holding long VIX call spreads saw massive returns as the VVIX spike indicated that the VIX itself was becoming volatile. For example, a trader buying a VIX 25 call when VIX was at 18 paid a low premium. When the VIX exploded to 65, that call traded deeply in-the-money. The VVIX surge signaled that market makers were aggressively repricing the risk of further volatility shocks, driving up the premiums of all VIX derivatives.
When Traders Use It
Traders use the VVIX to gauge the tail risk in the volatility market. Volatility traders and option market makers use VVIX to size their VIX option positions. When the VVIX is low, VIX options are cheap, presenting an asymmetric opportunity to buy VIX calls as a portfolio hedge. Macro traders monitor the VVIX to identify regime shifts. A sudden spike in VVIX without a corresponding spike in the VIX often precedes major market dislocations, signaling that institutional desks are quietly buying volatility protection.
Limitations and Common Misconceptions
The VVIX does not predict the direction of the stock market; it predicts the behavior of the VIX. A common misconception is that a high VVIX means the market will crash. A high VVIX means the VIX is expected to move violently, which includes the possibility of a sharp VIX drop if a panic subsides quickly. Additionally, VVIX is heavily influenced by the structural skew of VIX options. Because VIX calls are systematically overpriced due to persistent hedging demand, the VVIX carries a structural premium that makes historical comparisons misleading without context.