Vanna
Vanna was a second-order options Greek measuring the rate of change of delta with respect to implied volatility, or equivalently the rate of change of vega with respect to the underlying price, indicating how an option's delta would shift if implied volatility changed and how its vega would shift as the underlying moved.
Vanna occupied a cross-derivative position in the options Greek hierarchy: it connected delta (a first-order Greek measuring sensitivity to price) with implied volatility (another dimension of the options surface). Mathematically, it was the second partial derivative of the option's value with respect to both the underlying price and implied volatility simultaneously. This dual identity — as DdeltaDvol and also DvegaDspot — made vanna central to understanding how options positions behaved when price and volatility moved together, which was the common case in equity markets.
In equity markets, price and implied volatility were typically negatively correlated: when Nifty fell, India VIX and implied volatility generally rose. This negative correlation made vanna a highly relevant Greek for Indian index options holders. A long put position had negative vanna in many configurations — as Nifty fell (benefiting the put) and implied volatility simultaneously rose (also benefiting the put), the put's delta moved more negative than a flat-IV world would predict. This vanna-driven delta increase amplified the put's response to a market decline accompanied by a volatility spike, a scenario that played out during India's March 2020 COVID crash.
For options market makers managing large books on NSE, vanna was a key risk sensitivity tracked alongside delta, gamma, and vega. A market maker who was net short vanna would be hurt when large moves in the index were accompanied by volatility spikes, because the delta of their short options would move more aggressively than expected, requiring larger and more costly delta hedges. Conversely, a long-vanna book benefited from the amplified delta movement in crash scenarios.
The practical relevance of vanna extended to the management of the volatility surface. Because vanna linked vega to spot movement, a delta hedge that did not account for vanna would become inaccurate as the underlying moved significantly, particularly when the volatility surface shifted at the same time. Professional volatility desks performing vanna-aware hedging adjusted their delta and vega hedges simultaneously to account for the cross-sensitivity.
India's pronounced put skew — where OTM puts carried substantially higher IV than OTM calls — amplified vanna effects at the lower end of the strike distribution. During sharp Nifty drawdowns, OTM puts went from having modest delta to large delta not only because they moved toward ITM status but also because the simultaneous spike in IV further boosted their delta through the vanna channel. Risk managers at domestic institutions and FPIs with large Nifty put books monitored vanna exposure as part of their tail-risk assessment.