Vanna Greek Explained: How Volatility Affects Your Delta

Vanna is a second-order Greek that connects two of the most important concepts in options: delta and volatility. While many traders understand how delta changes with price (gamma) and how options prices change with volatility (vega), fewer understand vanna and its powerful effects on markets. In this guide, we will explore vanna in depth and show how understanding it can improve your trading.

What is Vanna?

Vanna measures how much delta changes when implied volatility changes. It can also be viewed as how much vega changes when the underlying price changes. Mathematically, vanna is a cross-partial derivative.

For out-of-the-money options, vanna is typically positive. This means when volatility rises, OTM options gain delta (become more sensitive to price moves). When volatility falls, OTM options lose delta.

Understanding Vanna Intuitively

Think about an out-of-the-money call option. In a low volatility environment, the chance of it finishing in the money is small, so it has low delta. But if volatility suddenly increases, there is a greater chance the stock could make a big move, increasing the probability the option finishes ITM. This higher probability means higher delta.

Vanna quantifies this relationship. A vanna of 0.02 means that for every 1% increase in implied volatility, delta increases by 0.02.

Vanna Characteristics

Vanna by Moneyness

• ATM options: Vanna is close to zero because delta is already around 0.50 and relatively stable
• OTM options: Vanna is positive and largest for calls, meaning rising IV increases delta
• ITM options: Vanna is negative for calls, meaning rising IV decreases delta (pulls it back from 1.0)

Vanna and Puts

For puts, the signs are opposite. OTM puts have negative vanna (rising IV makes delta more negative). ITM puts have positive vanna (rising IV makes delta less negative, closer to zero).

Vanna Flows and Market Impact

Vanna has become increasingly important in understanding market dynamics, particularly around market makers' hedging activities. When dealers are short options (long gamma but also exposed to vanna), changes in volatility force them to adjust their delta hedges.

The Vanna Rally

When volatility drops (like after a market selloff stabilizes):

• OTM calls lose delta (vanna effect)
• Market makers who are short these calls were hedged with short stock
• As call delta drops, they need less short hedge
• They buy back stock to reduce their hedge
• This buying pressure pushes prices higher

This creates a positive feedback loop where falling volatility leads to buying, which pushes prices up, which further reduces volatility.

The Vanna Selloff

The opposite occurs when volatility spikes:

• OTM puts gain delta (become more negative)
• Market makers short puts need to sell more stock to hedge
• This selling pressure pushes prices lower
• Lower prices increase volatility further

This explains some of the accelerated selloffs we see during market panics.

Trading Strategies Using Vanna

1. Vanna Scalping

Similar to gamma scalping, but focused on volatility changes. Buy options when you expect volatility to rise, capturing both the vega gain and the delta increase from vanna.

2. Skew Trading

The volatility skew (different IVs at different strikes) is closely related to vanna. Trading the skew can involve positioning for changes in the vanna exposure across strikes.

3. Vol Surface Arbitrage

Professional traders look for mispricings in the volatility surface that violate vanna relationships. These are advanced strategies requiring sophisticated tools.

Vanna in Your Portfolio

To calculate your portfolio vanna, sum the vanna of each position:

Vanna vs Charm

While vanna measures how delta changes with volatility, charm measures how delta changes with time. Both are important for understanding delta dynamics:

• Vanna: Delta sensitivity to implied volatility
• Charm: Delta sensitivity to time
• Gamma: Delta sensitivity to price

Together, these second-order Greeks give you a complete picture of how your delta exposure will evolve.

Practical Tips for Managing Vanna

• Know your exposure: Calculate portfolio vanna before volatility events
• Watch VIX: Changes in VIX (market volatility index) affect individual stock IV and thus vanna
• Consider skew: Different strikes have different vanna, affecting your total exposure
• Hedge when needed: Large vanna exposure can cause unexpected delta swings
• Use spreads: Spreads can reduce vanna exposure compared to naked options

When Vanna Matters Most

Vanna exposure is particularly important during:

• Earnings season: IV changes dramatically around announcements
• Market corrections: Volatility spikes cause large vanna-driven flows
• Volatility mean reversion: After elevated vol, the drop causes vanna effects
• Options expiration: Dealers adjust hedges as gamma and vanna exposure changes

Summary

Vanna is a powerful second-order Greek that explains how your delta changes when implied volatility moves. Understanding vanna helps you anticipate delta swings during volatility events and explains some market phenomena like vanna-driven rallies and selloffs. While more complex than the first-order Greeks, vanna is essential knowledge for sophisticated options traders. Monitor your portfolio vanna, especially before earnings and during market stress, to avoid unexpected exposure changes.

Continue learning about advanced Greeks with our guides on charm and volga.