Vanna and charm, the second-order Greeks

Delta, gamma, theta, vega, and rho get most of the attention, and for good reason, they explain the majority of an option's price behavior. But there's a second layer beneath them: second-order Greeks, which measure how the first-order Greeks themselves change. Two of the most useful ones for active traders are vanna and charm.

What second-order Greeks actually measure

A first-order Greek like delta tells you how much an option's price changes for a $1 move in the stock. A second-order Greek tells you how much that first-order Greek itself changes when something else moves. Gamma is technically the most well-known second-order Greek already, since it measures how delta changes as the stock price moves. Vanna and charm extend that same idea to two other inputs: implied volatility and time.

Vanna: how delta changes with volatility

Vanna measures how much an option's delta changes when implied volatility changes, holding the stock price constant. It also works in reverse: how much vega changes when the stock price moves.

This matters most for out-of-the-money options. When implied volatility rises, an out-of-the-money option starts behaving more like an at-the-money option, meaning its delta increases, even if the stock hasn't moved at all. This is vanna in action. A trader holding a position with meaningful vanna exposure can see their directional exposure shift purely because volatility moved, not because the stock did.

This becomes especially relevant around known volatility events. Heading into earnings or a Fed decision, implied volatility often rises in advance, which can quietly increase the delta of out-of-the-money options a trader is holding, changing the position's directional risk before the event even happens.

Charm: how delta changes with time

Charm measures how much an option's delta changes purely from the passage of time, holding the stock price and volatility constant. It's sometimes called "delta decay."

As expiration approaches, an out-of-the-money option's delta tends to drift toward zero, while an in-the-money option's delta tends to drift toward 1 for calls or negative 1 for puts. This happens simply because there's less time left for the stock to move, so the market becomes more confident about whether the option will expire in or out of the money. Charm quantifies how fast that drift happens.

Charm effects are strongest in the final days before expiration, and they accelerate through the last week. This is one of the reasons short-dated options positions can feel like their directional exposure is shifting under you even when the stock is barely moving.

Why this matters for active traders

Most retail traders never need to calculate vanna or charm directly. But understanding what they represent explains real behavior that otherwise looks confusing: a delta-neutral position that stops being delta-neutral overnight with no stock movement, or a hedge that needs constant adjustment during the final week before expiration.

Traders running larger or more complex multi-leg positions, especially those trying to hold a delta-neutral or gamma-neutral stance over time, benefit from knowing that vega and time decay aren't just affecting the position's value directly, they're also quietly reshaping its directional exposure through vanna and charm.

There's also a market-wide angle. Large options market makers hedge enormous vanna and charm exposure across the entire market, and their hedging flows around major expiration dates and volatility events are believed by many market participants to contribute to broader price action, particularly heading into monthly and quarterly options expiration.

A practical way to think about it

If gamma tells you your delta is unstable as the stock moves, vanna tells you your delta is unstable as volatility moves, and charm tells you your delta is unstable simply because time is passing. All three chip away at the assumption that a position's directional exposure is fixed once it's opened.

Frequently asked questions

Do I need to calculate vanna and charm myself to trade options?

No. Most retail traders don't calculate these directly, but understanding the concept helps explain why a position's delta shifts even when the stock price hasn't moved.

Which options are most affected by vanna and charm?

Out-of-the-money options tend to show the largest vanna effects, and options close to expiration tend to show the largest charm effects.

Are vanna and charm only relevant for market makers?

They're most heavily used by market makers and institutional desks for hedging, but any trader holding multi-leg or longer-dated positions benefits from understanding how these forces can quietly change a position's risk profile.

Related: Delta, Delta hedging, Greeks near expiration, Long gamma vs short gamma