Vanna Exposure measures how dealer delta hedges respond to changes in implied volatility (IV). Unlike gamma, which captures sensitivity to price, vanna reveals the volatility-price feedback loop that drives many market dislocations.

What is Vanna?

Vanna is a second-order Greek measuring the rate of change of delta with respect to implied volatility:

$\text{Vanna} = \frac{\partial \Delta}{\partial \sigma} = \frac{\partial \text{Vega}}{\partial S}$

In plain terms: when IV rises or falls, option deltas shift, forcing dealers to re-hedge.

Why Vanna Exposure Matters

Consider a market with significant put open interest. If IV spikes (a "vol-up" event):

1. Put deltas become more negative
2. Dealers who are short puts now have more negative delta exposure
3. They must sell the underlying to re-hedge
4. Selling pressure pushes prices lower
5. Lower prices → more IV → feedback loop

This vanna-driven cascade explains why selloffs can become self-reinforcing.

While the selloff example is the classic case, consider a market with significant call open interest. If IV drops (a "vol-down" event):

1. Call deltas become more positive
2. Dealers who are short calls now have more positive delta exposure
3. They must buy the underlying to re-hedge
4. Buying pressure pushes prices higher
5. Higher prices → lower IV → feedback loop

The Vanna Formula

For a single option:

$\text{Vanna} = \frac{-d_2}{\sigma} \times \frac{e^{-d_1^2/2}}{\sqrt{2\pi}} \times \frac{1}{S}$

Where $d_1$ and $d_2$ are the standard Black-Scholes terms.

Aggregate vanna exposure sums this across all strikes weighted by open interest, from the dealer's perspective.

Vanna Flows: The Mechanics

Scenario	Dealer Position	IV Change	Required Hedge	Market Impact
Short puts	Short vanna	IV ↑	Sell underlying	Bearish
Short puts	Short vanna	IV ↓	Buy underlying	Bullish
Short calls	Long vanna	IV ↑	Buy underlying	Bullish
Short calls	Long vanna	IV ↓	Sell underlying	Bearish

When Vanna Dominates

Vanna flows tend to matter most:

• Into and out of FOMC/CPI - IV expansion/contraction drives repositioning
• During volatility events - VIX spikes trigger cascading vanna hedges
• End of month/quarter - Systematic vol-selling unwinds
• Around large expirations - OTM options with high vanna sensitivity expire

Vanna vs. Gamma

Aspect	Gamma	Vanna
Sensitivity to	Price movement	Volatility movement
Peak exposure	At-the-money	Out-of-the-money
Dominant regime	Low IV, tight ranges	High IV, vol events
Time effect	Increases into expiry	Complex (interacts with charm)

Understanding both gives a complete picture of dealer hedging pressure.

VannaCharm's Approach

We calculate vanna exposure using per-strike implied volatility from a smoothed IV surface, not a flat vol assumption. This captures the skew dynamics that significantly affect OTM vanna calculations.

For technical details on our methodology, see: Improving Our Exposure Model With IV Surfaces

The Challenge in Simulating Vanna into the Future Vs. Gamma and Charm

In step forward simulations, gamma and charm exposures are relatively straightforward to calculate - you can recalculate gamma based on price, and recalculate charm based on time decay. Vanna, however, depends on changes in implied volatility, which are inherently more difficult to predict and model. This makes simulating vanna exposure more complex, as it requires assumptions about how implied volatility will evolve. This is an open effort here at VannaCharm as we work on possible step forward / future simulation models that incorporate custom volatility models in order to simulate vanna exposure more accurately.

Related Concepts

• Gamma Exposure (GEX) - Price-driven dealer hedging
• Charm Exposure (CEX) - Time-driven dealer hedging
• Implied Volatility Surface - The vol surface that drives vanna
• Volatility Regime - Market states where vanna dominates