Volatility of Volatility and Second Order Volatility Risk

Vol of vol is the volatility of implied volatility itself, captured by vanna and volga, second-order Greeks that matter even when vega is flat.

Volatility of volatility is exactly what the name says, the standard deviation of changes in implied or realised volatility itself over time, and it is a second-order risk that sits on top of ordinary vega exposure because a position’s sensitivity to volatility is not constant. A book can be flat first-order vega and still carry a large exposure to how much volatility itself moves, captured by the second-order Greeks vanna and volga.

The most direct tradable read on the quantity is the VVIX index, which applies the same variance-swap replication described in the VIX calculation to options on VIX futures rather than to options on the S&P 500 itself, producing an implied volatility of implied volatility. VVIX has historically traded in a range roughly between 80 and 100 during calm periods and has spiked well above 130 during episodes of acute stress, a wider relative range than VIX itself typically covers, which reflects how much less stable volatility’s own level is compared with the underlying it is measuring.

Vanna measures how a position’s delta changes as implied volatility moves, equivalently how its vega changes as the underlying’s spot price moves, and it matters because spot and implied volatility on an equity index do not move independently. The same leverage effect that makes index skew slope downward means a falling spot typically arrives together with rising implied volatility, so a book with meaningful vanna needs its hedge ratio adjusted for that joint move rather than for a change in spot or in volatility considered on its own. This cross term is a standing risk factor on any book of index or FX options, where spot-vol correlation is persistent enough to be treated as a market input…

Volga measures how a position’s vega itself changes as implied volatility moves, the second derivative of the option’s value with respect to volatility rather than the first, and a position with positive volga gains from a large move in implied volatility in either direction, up or down, beyond what a linear vega estimate would predict. This convexity is priced most visibly in the wings of the volatility surface rather than at the at-the-money point, and it is the basis of the vanna-volga method used to interpolate an entire foreign-exchange volatility smile from just three market-quoted points, the at-the-money level, the risk reversal and the butterfly, by adjusting a Black-Scholes price…

VIX options give a desk direct access to volga and vanna exposure on volatility itself rather than on the underlying index, since their payoff depends on where implied volatility, expressed through the VIX, ends up rather than where the S&P 500 ends up. A book that is long volga on its index options profits from implied volatility whipping around sharply, even if the level ends the period roughly where it started, a distinct exposure from a pure vega position that only cares about the net change in the level over the same period.