SVQ · Greeks
Charm
Also called: delta decay, DdeltaDtime
Charm, or delta decay, measures how an option's delta changes as time passes with price and volatility held fixed.
Definition
Charm is the rate of change of an option's delta with respect to the passage of time. It is a second-order Greek, the cross derivative of option value with respect to the underlying price and time.
It explains why a delta hedge drifts overnight, or through a trading session, even if nothing else changes.
Intuition
As expiry approaches, uncertainty shrinks. An out-of-the-money option becomes more certain to expire worthless, so its delta drifts towards zero; an in-the-money option becomes more certain to finish in the money, so its delta drifts towards one (or minus one for puts).
For hedgers, charm means the hedge must be adjusted just because the clock moved. Aggregated across a dealer book, especially near expiry, those adjustments can create predictable-looking hedging flows in the underlying.
How it's calculated
Charm = ∂Δ / ∂t = −∂Δ / ∂T
where t is calendar time and T is time to expiry. In Black–Scholes with zero rates and dividends, for a call:
Charm = φ(d1) · d2 / (2T)
with φ the standard normal density. With non-zero rates and dividends extra terms appear. Sign conventions differ across sources (per year versus per day, ∂/∂t versus ∂/∂T), so always check which one a tool uses; dividing an annualized value by 365 gives an approximate per-day change.
Example: a call with delta 0.30 and charm of −0.02 per day will, all else equal, have a delta near 0.28 tomorrow. A dealer short 1,000 such contracts with a 100-share multiplier, hedged long 30,000 shares, would need to sell about 2,000 shares just because a day passed.
How to read it
Charm grows sharply in the final days and hours before expiry, when deltas of near-the-money options swing between zero and one. That is why delta decay matters most for short-dated and same-day options.
Positive charm on a long position means delta will rise as time passes, all else equal; negative charm means it will fall. For a dealer hedging customer flow, the sign of the book's charm indicates whether time decay alone will force buying or selling of the underlying.
Common mistakes
- Ignoring sign conventions and reading a per-year number as per-day, or the reverse.
- Assuming charm is small and stable; near expiry it dominates delta changes.
- Treating modeled dealer hedge flows as certain. They depend on assumed positioning.
- Forgetting weekends and holidays when converting time decay into calendar days.
In Saqrid
SVQ's docked Greek heatmaps include charm alongside vanna, volga, speed, color, zomma and ultima.
TEP Charm is a same-day-expiry hedge schedule that shows modeled dealer hedge flow at each Eastern-time clock point.
Open SVQ.
Go deeper
Saqrid Institute lesson: Hedging & the Greeks II: Rho, Vanna, Charm, Volga. Lesson text is open to read without an account.