Volga (Vomma)
The convexity of vega to volatility
Volga — also called vomma — measures how vega itself changes as implied volatility moves. If vega is the first derivative with respect to volatility, volga is the second: it describes the convexity of an option to volatility.
What It Tells You
An option with positive volga becomes more sensitive to volatility as volatility rises. That means a long option position gains from a volatility spike at an accelerating rate, not a linear one. Volga is largest for out-of-the-money options with meaningful time remaining — exactly the contracts used for tail hedging.
Why Tail Hedges Work the Way They Do
Deep out-of-the-money puts appear to do nothing for long stretches and then pay disproportionately in a crisis. Part of that payoff is delta, but a substantial part is volga: the volatility spike accompanying the selloff makes the option more sensitive to that same spike. It is the mathematical basis of convex hedging strategies.
The Cost Side
Convexity is never free. Options with high volga carry a volatility risk premium priced into them, which is why systematically buying tail protection has a persistent cost in calm markets. Volga explains both why the payoff is so large when it works and why the carry is so painful when it does not.