Vanna and Volga Effects

Vanna and Volga are second-order derivatives sensitivities, often called higher-order Greeks, that describe how option prices change when volatility itself changes. Vanna measures the sensitivity of an option Delta to changes in implied volatility, indicating how the hedge ratio must be adjusted as market fear or uncertainty shifts.

Volga, also known as Vomma, measures the sensitivity of an option Vega to changes in implied volatility, revealing how the option's exposure to volatility changes as volatility levels move. In cryptocurrency markets, where volatility is often extreme and regime-dependent, these effects are critical for market makers managing tail risk.

When Vanna is high, a market maker's directional hedge becomes unstable during volatility spikes, forcing them to buy or sell the underlying asset rapidly. Volga determines the convexity of the Vega position, meaning the cost of maintaining a volatility-neutral stance accelerates as volatility moves further away from the current level.

Together, they explain the feedback loops where volatility shifts force delta hedging, which in turn moves the spot price and triggers further volatility changes. Mastering these effects is essential for understanding why liquidity often evaporates during crypto market crashes.

They represent the mathematical bridge between static risk management and the dynamic reality of liquidity provision in non-linear derivative markets.