Volga
Volga, also known as vomma or DvegaDvol, was a second-order options Greek measuring the rate of change of vega with respect to implied volatility, indicating the convexity of an option's value with respect to volatility and quantifying how rapidly vega itself would increase or decrease as implied volatility moved.
Just as gamma measured the convexity of an option's price with respect to the underlying (making long gamma positions benefit from large moves), volga measured the convexity of an option's vega with respect to implied volatility. A position with positive volga gained vega as IV rose — and since higher IV generally meant more expensive options, a long-volga position benefited disproportionately from volatility-of-volatility scenarios where IV moved significantly.
Volga was largest for options that were significantly out-of-the-money. An ATM option's vega was relatively stable regardless of small changes in IV — its volga was low. A deep OTM option's vega was very sensitive to changes in IV: at very low IV, the OTM option was essentially worthless with near-zero vega; at high IV, the same option gained significant vega as it came closer to being ATM in volatility-adjusted terms. This sensitivity — the rapid increase in vega as IV expanded — was captured by volga.
In the Indian context, deep OTM Nifty put options were the primary instruments with meaningful volga. During normal market periods, these far-OTM puts had minimal vega because their probability of expiring in the money was very low. When volatility spiked during a market stress event — as happened during the March 2020 COVID-19 crash, the 2022 global rate shock, or election-related uncertainty periods — India VIX rose sharply, and deep OTM puts experienced an explosive increase in vega through the volga channel. Their prices moved far more than a simple linear vega calculation would suggest, because their vega itself expanded as IV rose.
For options sellers, volga represented a hidden risk in out-of-the-money positions. Selling deep OTM puts appeared to collect modest premium with low sensitivity to small IV changes. However, in a severe volatility spike, the rapid vega expansion through volga made these positions far more expensive to close or hedge than a first-order vega analysis would predict. This non-linearity was part of the reason professional risk managers on Indian options desks used second-order Greeks rather than relying solely on vega for options book risk quantification.
Strategies deliberately designed to capture volga exposure — long volatility-of-volatility positions — involved owning deep OTM options or option structures that benefited from large moves in IV itself. These were sometimes called vol-of-vol trades and were the domain of specialist volatility arbitrage desks rather than typical retail options participants.