Vanna
Vanna measures how an option's delta shifts when volatility changes. Learn why it links direction and volatility, and why hedgers cannot ignore it.
Vanna measures how an option's delta changes when volatility moves. It is the bridge between two forces that beginners treat as separate: direction and volatility. A change in the market's fear level quietly shifts how directional your option is.
It is a second-order Greek, and it works in two directions at once. Let me untangle what that means.
The Bridge Between Delta and Vega
Vanna connects delta and vega. It answers two questions that turn out to be the same one: how much does my delta change when volatility moves, and how much does my vega change when the stock moves?
Picture an out-of-the-money call. When volatility is low, it has little chance of finishing in the money, so its delta is small. Now let volatility rise. Suddenly a big move looks plausible, the option's odds of finishing in the money improve, and its delta climbs, even though the stock has not budged. That shift in delta, driven purely by a change in volatility, is vanna.
Two Views of the Same Number
The elegant thing about vanna is that it describes one relationship you can read from either side.
From the delta side: vanna is how much your delta changes when volatility shifts. Rising volatility fattens the delta of out-of-the-money options.
From the vega side: vanna is how much your vega changes when the stock moves. As the stock travels toward a strike, that option's sensitivity to volatility changes too.
Both are the same cross-effect between price and volatility, just viewed from opposite ends. That is why vanna feels slippery at first. Once you see it as a single link between direction and volatility, it clicks.
Why It Matters
Vanna is a headache for anyone running a delta-neutral book, and a tool for those who understand it.
A hedge that is delta neutral at today's volatility will not stay neutral if volatility moves, because vanna shifts the deltas. A trader who balanced their position in a calm market can find it leaning directional the moment fear spikes. Ignoring vanna means your hedge silently breaks exactly when markets get wild.
It also shapes real market behavior. The skew in option prices means vanna is not symmetric, and large dealer positions in vanna can influence how the market moves as volatility changes. For most traders, the key insight is humbler but important: direction and volatility are not independent, and vanna is the reason your delta and your vega keep talking to each other.
- Vanna is how delta changes when volatility moves.
- It is also how vega changes when the stock moves, the same link both ways.
- Rising volatility fattens the delta of out-of-the-money options.
- It breaks a delta-neutral hedge when volatility shifts.
Pop Quiz
Three quick questions to see what stuck. Pick an answer and the explanation shows up right away.
What does vanna measure?
Vanna links delta and volatility: it is the change in delta for a change in volatility.
Volatility rises while an out-of-the-money call's stock stays flat. What happens to its delta?
Higher volatility makes a big move more plausible, raising the option's delta even with a flat stock.
Why does vanna trouble a delta-neutral hedge?
Because vanna changes delta when volatility moves, a hedge balanced at one volatility drifts off when volatility shifts.
Bottom Line
Vanna is the handshake between direction and volatility. It measures how your delta shifts when volatility moves, which is the very same thing as how your vega shifts when the stock moves. One number, two views, tying together two forces that are not really separate.
For hedgers it is a live risk: a delta-neutral book quietly tilts directional whenever volatility changes. Even if you never hedge, vanna is the reason you cannot think about direction and volatility in isolation.
Keep going: the two Greeks it links are delta and vega, and the balance it disturbs is delta neutral.