Vanna is a second-order option Greek measuring the sensitivity of an option's Delta to changes in Implied Volatility ($\frac{\partial \Delta}{\partial \sigma}$). When Implied Volatility (IV) drops during market rallies, positive Vanna causes out-of-the-money put deltas to shrink rapidly, forcing market makers to buy futures to rehedge. This mechanical feedback loop generates explosive, low-volatility melt-ups in equity indices like NIFTY 50.
In Black-Scholes-Merton option pricing, Vanna is the partial cross-derivative of option price with respect to spot price ($S$) and volatility ($\sigma$):
Where $d_1$ and $d_2$ are standard Black-Scholes cumulative distribution parameters, $n(d_1)$ is the standard normal probability density function, and $\sigma$ is annualised implied volatility.
Vanna plays a pivotal role during major market turnarounds: