Model the Flows · Lesson 1 of 9
Vanna and Charm
How changes in implied volatility and the simple passing of time shift dealer hedges, even when price stands still.
In this lesson
- Explain how vanna and charm change delta with no move in price
- Trace how falling implied volatility or passing time changes modeled dealer hedges
- Describe OPEX and holiday drift as debated tendencies, not laws
- Spot the conditions that weaken or reverse these flows
Earlier lessons showed that dealers hedge an option’s delta by trading shares, and that gamma makes them re-hedge when price moves. Price isn’t the only input that moves delta, though. Delta also shifts when implied volatility changes and when time passes, even if price stands perfectly still. The Greeks that measure those two effects are vanna and charm. Traders call them second-order Greeks because each one describes how a first-order Greek, delta, changes. Together they help explain why hedging flows can show up on quiet days with no news.
Vanna: volatility moves delta
Vanna measures how much delta changes when implied volatility (IV) moves one point. The intuition is simple. Higher IV widens the range of prices the market treats as possible, so an out-of-the-money option has a better chance of finishing in the money, and its delta grows. Lower IV narrows that range, and out-of-the-money deltas shrink toward zero. At-the-money deltas hardly move either way, so vanna is near zero at the money and largest for moderately out-of-the-money options. Now add the model’s dealer-side sign assumption: dealers are treated as short puts and long calls. Both positions give the dealer positive delta, so both are hedged with short stock. When IV falls, those out-of-the-money deltas shrink, the dealer needs less short stock, and the hedge adjustment is buying. When IV rises, the adjustment is selling. That second case matters in sell-offs, when IV usually jumps: vanna can add hedge selling on top of the gamma hedging you met earlier.
Example Vanna with numbers
SPY is at $500. Suppose the model has dealers short 20,000 contracts of the $480 put with 10 days left. At 25% IV, that put’s delta is about −0.16, so the dealer position carries roughly 20,000 × 100 × 0.16 = 320,000 shares of delta, hedged with about 320,000 shares short. Now a scare fades and IV drops to 18% while price stays at $500. The put’s delta falls to about −0.08, so the hedge needs only about 160,000 shares short. Roughly 160,000 shares, about $80 million, get bought back without price moving at all. These figures are hypothetical, from a standard pricing model.
Before a scheduled event
Ahead of a Fed decision, IV is often elevated because the outcome is unknown. Out-of-the-money puts carry larger deltas, so the modeled dealer hedge holds more short stock.
The announcement
The news lands and the uncertainty is gone. IV can drop several points within minutes, a quick version of IV crush, even if price barely moves.
The hedge adjustment
Smaller deltas mean the modeled dealer needs less short stock, so the adjustment is buying. Some traders attribute part of a post-event drift higher to this.
What traders watch
Whether IV keeps falling after the announcement, and whether the regime stays Calm. If the news is a shock, IV rises instead and the same mechanism adds selling.
Charm: the clock moves delta
Charm measures how delta changes as time passes, with price and IV unchanged. As expiration gets closer, an out-of-the-money option’s delta decays toward zero, while an in-the-money option’s delta moves toward 1, or −1 for a put. The decay is slow with weeks left, faster in the final days, and hour by hour on expiration day. Under the same sign assumption, hedges against out-of-the-money puts and calls shrink as the clock runs, so the adjustment is buying. Say the model has dealers short 10,000 contracts of SPY’s $490 put, with SPY at $500 and IV at 18%. The put’s delta is about −0.24 with 10 days left and about −0.11 with 3 days left. That’s roughly 130,000 shares, around $65 million, of short hedge bought back in one calendar week with no change in price. In-the-money options work the other way: their deltas grow, and the adjustment is selling. Which side wins depends on where open interest sits relative to price.
Note OPEX and holiday drift: a debated idea
Put vanna and charm together and you get an idea many traders discuss. In the days before a large OPEX, IV often drifts lower and time decay speeds up. When most open interest is out of the money and the sign assumption holds, both effects point toward dealers buying back hedges. Some traders link this to a mild upward drift into monthly expiration. A similar story is told about long holiday weekends: many option models count calendar days, so three or four days of decay pass while the market is closed, and IV is often marked lower beforehand. Treat both as hypotheses, not laws. Researchers and practitioners disagree on how large the effects are, and news, earnings or economic data can swamp them on any given day. On StratosHedge, key levels come from the nearest expiration, so a monthly’s vanna and charm don’t shape them until expiration day itself.
When the story tends to hold
- Most open interest sits out of the money, on both sides of price, so time and falling IV shrink the deltas being hedged
- Customers are net buyers of puts and net sellers of calls, so the dealer-side sign assumption fits
- IV is elevated after a scare and has room to fall
- No major scheduled event lands before expiration, so nothing props IV up
When it tends to fade or reverse
- Most open interest is in the money, so deltas grow as time passes and the adjustment is selling
- Customers are heavy put sellers or call buyers, so the sign assumption is off and the hedge direction flips
- IV is already low, with little room left to fall
- A Fed decision or inflation report keeps IV elevated until it passes
Check your understanding
5 questions. Answer each one, then open “Show answer” to compare.
Show answer
Answer: B. Implied volatility changes
Vanna links delta and implied volatility. Delta’s response to price is gamma, its response to time is charm, and rho measures sensitivity to rates.
Show answer
Answer: B. Dealers buy back some short stock, because the puts’ deltas shrink
Lower IV shrinks out-of-the-money deltas. A short put gives the dealer positive delta hedged with short stock, so a smaller delta means less short stock is needed, and the adjustment is buying. That’s vanna at work with no price move.
Show answer
Answer: False.
Charm shrinks out-of-the-money deltas but grows in-the-money ones, so the direction depends on where open interest sits relative to price. It also depends on the dealer-side sign assumption, which can be wrong.
Question 4 of 5 The model has dealers short 10,000 put contracts. Over one week, with price and IV unchanged, the put’s delta goes from −0.24 to −0.11. About how many shares of short hedge get bought back?
sharesShow answer
Answer: 130000 shares (anything within ±5000 shares counts).
The delta change is 0.24 − 0.11 = 0.13. Multiply by 100 shares per contract and 10,000 contracts: 0.13 × 100 × 10,000 = 130,000 shares, all from time passing.
Show answer
Answers: A. Most open interest is in the money · B. Customers are heavy put sellers, so the sign assumption is wrong · C. A Fed decision keeps IV elevated until it passes
In-the-money deltas grow as time passes, a wrong sign assumption flips the hedge direction, and a pending event stops IV from falling. Elevated IV that is starting to fall is the condition where the supportive vanna story most often applies, so it doesn’t weaken it.
Key takeaways
- Vanna is delta’s response to implied volatility; charm is delta’s response to time.
- Under the dealer-side sign assumption, falling IV and passing time tend to shrink hedges on out-of-the-money options, which shows up as buying.
- In-the-money open interest, a wrong sign assumption or a pending event can weaken or reverse the effect.
- OPEX and holiday drift are debated tendencies; use them to explain hedging, not as a calendar to trade.
Try it in StratosHedge
Add the Symbol & GEX Overview panel to a dashboard layout to see modeled vanna and charm totals next to GEX, DEX, VEX and TEX. These totals cover only the nearest expiration (0DTE for SPY on most days), so watch how the charm total changes through the afternoon, not across weeks, and remember they rest on the same dealer-side sign assumption.
See vanna and charm totals Needs: Retail plan
Key terms
- Delta
- How much an option’s price changes for a $1 move in the underlying. A 0.50 delta call gains about $0.50 per share ($50 per contract) on a $1 rise.
- Gamma
- How fast delta changes for a $1 move in the underlying. It’s largest for at-the-money options close to expiration.
- Implied volatility (IV)
- The future volatility that option prices imply, quoted as an annual percentage. Higher IV means pricier options.
- Vanna
- How delta changes when implied volatility changes. It means dealer hedges can shift even while price stands still.
- Charm
- How delta changes as time passes, with price and volatility unchanged. It speeds up near expiration and can shift dealer hedging late in the day.
- Second-order Greeks
- Greeks that describe how a first-order Greek changes. Vanna (delta’s response to implied volatility) and charm (delta’s response to time) are the most discussed in dealer hedging.
- Dealer-side sign assumption
- The model’s assumption that dealers are net long calls and net short puts, so calls count as positive gamma and puts as negative.
- IV crush
- A sharp drop in implied volatility after a known event such as earnings passes, which deflates option prices even if the stock moves.
- Expiration
- The date an option contract ends. After it, the contract no longer exists and any remaining rights are gone.
- OPEX (options expiration)
- Options expiration day, most often the monthly standard expiration on the third Friday. Large amounts of open interest can expire at once and reshape the map.
- Rho
- How much an option’s price changes for a 1-percentage-point change in interest rates. It matters most for long-dated options.
Sources and further reading
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