Summary. Delta and gamma describe how an option's risk changes when price moves. Vanna and charm describe how it changes when price does not: vanna when implied volatility moves, charm when time passes. Both force dealers to adjust their hedges, and both show most on days when little else is happening. This guide defines each greek, shows why the two are closely related, explains when each one dominates dealer hedging, and describes how they interact around monthly expiration.
1. The definitions
Vanna is the rate at which an option's delta changes when implied volatility changes, and equally the rate at which vega changes when the underlying moves:
If implied volatility falls by a point, most deltas in the chain shift, and a dealer hedged at the old deltas now holds the wrong hedge. Vanna measures that mismatch.
Charm is the rate at which delta changes as time passes, with the underlying and implied volatility held fixed, where is elapsed time:
As expiration approaches, an out-of-the-money delta drifts toward zero, and an in-the-money delta toward one for a call or minus one for a put, even if nothing else moves. Charm measures the speed of that drift.
Why the two are related
In the Black-Scholes model with zero interest rates and dividends, delta depends on time and implied volatility only through the expected move to expiry, , where is the time remaining. Time passing and implied volatility falling both shrink it, so they push delta the same way:
Charm is vanna multiplied by . Across strikes the two have the same shape with opposite signs, close to zero at the money and largest about one standard deviation either side; only the scale differs. In a hypothetical case with implied volatility at 16%, one day of time with twenty trading days left does to delta what a fall of about 0.4 points in implied volatility would. With two days left, the same day is worth almost 5 points. That is why charm hedging grows so quickly in the last days of an expiry, while vanna matters only when implied volatility actually moves.
2. When vanna dominates
Vanna becomes the main hedging flow when implied volatility moves a lot and the index moves little. The clearest case is the drop in implied volatility after a scheduled event resolves: a Federal Reserve decision, an inflation report or, for a single stock, earnings. The event premium drains out of the chain, and hedges sized for the old volatility are suddenly wrong.
Under the usual index positioning, dealers are short out-of-the-money puts bought for protection and long some out-of-the-money calls sold by customers writing calls for income, with short hedges against both. Lower implied volatility shrinks both deltas, so the dealer buys back part of each hedge. That buying is one explanation for the steady firming that often follows an uneventful Federal Reserve announcement.
The mechanism runs in reverse in a volatility shock. A sharp rise in implied volatility increases the absolute delta of the puts dealers are short, and they sell the index to rebalance. If the decline also takes spot below the gamma flip, gamma hedging sells too, one mechanism behind the rising-volatility, falling-index feedback of stressed sessions. After heavy customer call buying, dealer positions differ and the signs change, so a vanna estimate is only as good as the positioning estimate under it.
3. When charm dominates
Charm takes over when the index and implied volatility are both calm and the clock does the work, most cleanly on a quiet afternoon with no scheduled event ahead, in a long-gamma regime that keeps price contained. As out-of-the-money deltas decay, the hedges tied to them unwind:
- A dealer short calls holds a long hedge, and sells part of it as the calls' delta decays.
- A dealer short puts holds a short hedge, and buys part of it back as the puts' delta decays.
- A dealer long calls holds a short hedge, and also buys part of it back.
The net direction depends on which positions are larger. Under the usual positioning, the put side and any dealer-long calls both produce buying, which is the mechanical case for the often-cited drift higher into the close on quiet days. Heavy customer call buying puts the call side on the selling side instead. Charm on its own does not pull price toward the largest strike; that pull, where it exists, comes from long-gamma hedging around the strike.
4. Vanna and charm around monthly expiration
Monthly expiration is where both greeks matter at once. The expiring contracts carry the month's largest open interest, and as the third Friday approaches, charm on them grows quickly. If implied volatility also moves that week, around an inflation report, a Federal Reserve meeting or a cluster of large earnings releases, vanna resizes the same hedges on top of the charm flow.
The pin often seen near expiration comes from gamma: when dealers are long gamma at a heavily held strike, their hedging pulls price back toward it. Vanna and charm decide how much hedging is still attached to that strike in the final days. Ni, Pearson and Poteshman document that stock prices cluster at strike prices on expiration dates. For SPX the timing matters, because the standard monthly options settle on the third Friday's opening prices, while PM-settled contracts expiring that day settle at the close.
After expiration, the contracts that carried the most vanna and charm are gone with their hedges, and a smaller book of later expiries remains. That can leave the index less anchored in the following days, though whether it shows up as higher volatility depends on the positions that replace them.
5. Reading vanna and charm on an exposure map
- Size and sign by strike. The strikes with the largest absolute vanna and charm, signed by the dealer convention, show where a move in implied volatility, or another hour of decay, would change dealer hedges the most, and in which direction.
- Vega exposure is related but different. Vega exposure shows how much dealer books gain or lose when implied volatility moves; vanna shows how their hedge in the underlying changes, the more direct measure of the buying or selling that follows. On DataFirst, VEX means vanna exposure; some other charts use the same label for vega, so check which one a chart shows.
- The calendar. Vanna matters most around scheduled events that move implied volatility; charm in the last days of a large expiry and the last hours of each session.
Both are most useful on slow, drifting afternoons, when the market seems to be doing nothing and the clock and implied volatility are doing the work. The DataFirst terminal shows vanna and charm alongside gamma, and options market maker hedging sets all four hedging flows side by side.
For educational and informational purposes only. Not financial advice. Options trading involves substantial risk of loss. The numbers in the example are hypothetical, and the formulas assume Black-Scholes with zero rates and dividends.