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Key Takeaways
- Charm measures option delta’s response to the passage of time at fixed price and other model inputs.
- Aggregate charm using signed contract quantities to calculate the book’s delta drift.
- The stock-hedge adjustment has the opposite sign to the option book’s delta change.
- Read the result in hedge shares per calendar day: the example book’s −16,000 delta drift means buying 16,000 shares a day to stay flat.
- For the weekend, price delta at Friday’s and Monday’s inputs and hedge the difference, because charm itself changes across the weekend.
What is charm exposure?
Charm exposure is the total change in a signed option book’s delta as time advances while price and other model inputs stay fixed. It adds each position’s charm, the time sensitivity of option delta, across the book. The opposite share count is the stock adjustment that restores the combined delta.
Use one explicit convention: per-share delta change per calendar day. Positive quantities represent long contracts and negative quantities represent short contracts. For standard equity options, multiply by 100 to convert each position into share equivalents. Open interest counts contracts, so a public-chain estimate takes the long and short signs from a positioning model, and that sign sets the hedge direction.
Formula
Option delta drift per day = 100 × Σ(signed contracts × charm per day); stock-hedge change per day = −option delta drift per day- Use standard 100-share equity options and positive quantities for long contracts, negative quantities for shorts.
- Charm is the change in per-share delta for each calendar day that passes with price, volatility and the other inputs unchanged.
- Multiplying the share-equivalent rate by spot expresses the same rate in notional dollars per day.
- For a finite interval, calculate 100 × Σ[signed contracts × (ending delta − starting delta)] and take the opposite stock trade.
How is charm exposure calculated?
XYZ trades at $100 with a monthly expiration on Friday. A positioning model estimates dealers are net short 40,000 contracts of the 95 put and net short 10,000 contracts of the 105 call, each with the standard 100-share deliverable. Modeled charm is +0.006 delta per day for the 95 put and −0.008 delta per day for the 105 call.
- 95 put: −40,000 × 0.006 × 100 = −24,000 option share equivalents per day
- 105 call: −10,000 × −0.008 × 100 = +8,000 option share equivalents per day
- Net option delta drift: −16,000 share equivalents per day
- Opposite stock-hedge rate: +16,000 shares per day
At these inputs, time reduces the option book’s delta at a local rate of 16,000 share equivalents per day. Maintaining zero combined delta requires the opposite stock adjustment: buying at a local rate of 16,000 shares per day. Reprice both deltas for the actual interval being evaluated.
The puts contribute −24,000 share equivalents per day. The calls contribute +8,000. Net option delta drift is −16,000 per day, so the stock hedge buys at the opposite local rate of +16,000 shares per day.
For a full interval, calculate each option’s delta at both endpoints. Aggregate the signed delta differences and take the opposite stock trade. That directly measures the adjustment for the selected dates.
How charm changes near expiration
Away from the strike, in-the-money call deltas approach +1, in-the-money put deltas approach −1 and out-of-the-money deltas approach zero. Near the strike, the sensitivity to remaining time becomes concentrated.
At-the-money charm also comes from the pricing model. For a European call with spot and strike $100, 20% volatility and zero rates and dividends, Black-Scholes delta is 0.51 with 30 calendar days remaining and charm is −0.0002 per day. With one day remaining, delta is 0.50 and charm is −0.0010 per day, so the at-the-money drift per day grows as expiration closes in.
Price each position at its own strike, spot and remaining time, then weight its charm by its signed quantity: a large position near the strike in the final days drives the book’s drift.
How traders use charm exposure
Advance the pricing clock from Friday to Monday to calculate a weekend scenario. Apply the same model clock to every contract, then compare the projected hedge shares with underlying liquidity.
Use gamma exposure to study price-driven delta changes alongside this time-driven calculation. Compare the planned option position across target prices and dates in the options profit calculator.
Limitations of charm exposure
- Check the sign before trading the flow. Open interest counts contracts, so a public-chain estimate takes each side’s sign from a positioning model, and a flipped sign turns the example’s 16,000-share daily buy into a 16,000-share sell.
- Reprice for any interval longer than a day. The 16,000-share rate holds at today’s inputs and changes as expiration approaches, so price delta on Friday and again on Monday for the weekend hedge.
- Match the clock before comparing books. Calendar-day and trading-day charm give different numbers for the same position, so quote both books per calendar day.
- Reprice the positions near the strike as spot moves in the final days. Near expiration, charm concentrates around the strike, so a small move in spot can change the size and even the direction of a position’s delta drift.
Bottom line
Charm exposure is the hedging the clock forces while price stands still, and it runs biggest into weekends and expiration. Size that time-driven flow from the signed book, state the clock and sign conventions, and reprice delta at both dates for any full interval.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- OIC: Open Interest, Why It Matters
- OIC: Option Greek definitions
- OIC Options Glossary: Charm
- OIC: Delta
- Cboe Research: 0DTE Index Options and Market Volatility
- Cboe: Evaluating the Market Impact of SPX 0DTE Options
- CFA Institute: Valuation of Contingent Claims
How entries are sourced, calculated and updated: editorial methodology.