What Are Charm and Vanna? The Higher-Order Greeks That Move Markets

Most traders learn about delta, gamma, theta, and vega. Fewer learn about charm and vanna — the “second-order” Greeks. But these two are responsible for some of the most consistent patterns in index options markets, including end-of-day pinning and volatility-driven drift.

You don’t need to calculate them yourself. But knowing they exist helps explain why the market does what it does around OPEX and during vol regime shifts.

What are second-order Greeks?

First-order Greeks measure how an option’s price changes when something in the market changes. Delta measures price sensitivity to the underlying. Theta measures price sensitivity to time. Vega measures price sensitivity to volatility.

Second-order Greeks measure how the Greeks themselves change. Gamma is actually a second-order Greek — it measures how delta changes when price moves. Charm and vanna are two other second-order Greeks that track how delta changes in response to different inputs:

• Charm = how delta changes as time passes
• Vanna = how delta changes as implied volatility changes

Both of them force dealers to re-hedge without the underlying price doing anything. And that’s where the interesting market effects come from.

Charm: the time decay of delta

Charm is sometimes called “delta decay.” As an option approaches expiration, its delta drifts toward either 0 (if out of the money) or 1 (if in the money) — even if the underlying doesn’t move at all.

Imagine a call with a strike of 590 when SPY is at 595, with one week to expiration. The call has a delta of maybe 0.75. Now fast-forward to the day before expiration, SPY still at 595. That same call now has a delta closer to 0.95 — it’s clearly going to finish in the money, so it’s acting more like stock.

The delta changed without the underlying moving. That’s charm.

For dealers who hedged the original position, this creates a problem. Their old hedge was based on a delta of 0.75. Now the delta is 0.95, so their hedge is out of balance. They have to buy more underlying to catch up. And they have to do this continuously, all week, as charm pulls their deltas around.

This is why index markets often develop directional drift in the days leading up to expiration. Charm-driven hedging creates persistent buy or sell pressure that’s independent of any news. It’s mechanical.

Vanna: when volatility moves delta

Vanna measures how delta changes when implied volatility changes. When IV goes up, deltas of out-of-the-money options increase. When IV drops, they decrease.

Here’s the intuition. An out-of-the-money call has a low delta because there’s only a small chance it finishes in the money. But if implied volatility suddenly spikes, the market is now pricing in bigger expected moves, which means the call has a better chance of becoming in the money. Its delta goes up.

When IV compresses — which happens constantly during calm market periods and sharply after events — deltas of all those OTM options shrink. Dealers who were hedged to yesterday’s IV are now over-hedged, and they need to unwind stock positions to rebalance.

That unwinding creates buying pressure when vol is rising and selling pressure when vol is dropping. Which is one reason why calm markets tend to drift higher and volatile markets tend to slide — the vanna flow from dealer hedging reinforces the direction of volatility itself.

Why charm and vanna matter

The practical reason these matter is that they create mechanical, predictable dealer flow that doesn’t require any news, price move, or trader behavior. Just the passage of time (charm) or a change in IV (vanna) forces hedgers to rebalance.

A few well-known effects come from this:

• OPEX pinning — On monthly expiration days, charm pulls strike deltas toward 0 or 1 rapidly, forcing heavy hedging into specific levels. Price often gets magnetized to high-OI strikes through the morning.
• Quiet-market drift— During periods of low and falling volatility, vanna flow adds persistent buying pressure. This is part of the mechanism behind the famous “VIX is low, stocks grind up” pattern.
• Vol-shock cascades — When volatility suddenly jumps, vanna flow reverses — dealers have to sell stock to keep hedges balanced, which pushes the market down further, which pushes vol higher, and so on.

The practical takeaway

You’re not going to calculate charm and vanna at your desk. You don’t need to. But understanding them helps explain three things that otherwise feel mysterious:

1. Why the market sometimes drifts in one direction on quiet days with no news
2. Why monthly OPEX week has patterns that repeat month after month
3. Why vol spikes can feel self-reinforcing

When someone talks about “charm flow” or “vanna flow” around OPEX, they’re talking about the mechanical dealer hedging that happens because of these second-order Greeks. It’s not magic. It’s just math playing out in real time.

GammaFlux’s model accounts for these effects as part of estimating where dealer positioning is shifting intraday, alongside the gamma and delta flows that get most of the attention.