What is Charm (Delta Decay)?
Charm is the rate of change of an option's delta with respect to the passage of time. It is why options "pin" into expiration and why dealer hedges flow even on quiet days.
Definition
Charm is ∂Δ/∂t — how much an option's delta moves per day, holding everything else constant. OTM options see their delta decay toward zero as expiry approaches (their probability of ending ITM drops); ITM options see their delta drift toward 1 (they're almost certain to be exercised). At-the-money options, the most interesting case, have charm that flips sign as expiry comes: above the strike, delta drifts up; below it, delta drifts down. This creates a self-stabilising "pin" effect: when spot is near a high-OI strike going into expiration, dealer hedges flow in such a way that they tend to absorb moves away from the strike.
Why it matters & how it's calculated
Under a standard pricing model, charm for a call is −φ(d₁) · [2(r−q)T − d₂·σ·√T] / (2T·σ·√T) plus a small drift term. The key insight is not the formula but the structural behaviour: charm is highest in the last few days of life, and it cuts hardest into Friday-afternoon hedging flows. On a desk running a delta-hedged short-gamma book into expiration, you may need to trade thousands of shares per day purely to compensate for charm — even if spot is dead flat. This is why Friday afternoons on heavy-OI strikes are noisy in ways that pure spot-move models can't explain. The "vanna-charm flow" framework — popularised in the post-2018 literature — treats both Greeks as systematic hedging-flow drivers that can be forecast hours in advance from positioning data. Combined with weekend gamma roll-down, they explain a meaningful chunk of Monday-morning open-to-close drift on quiet weekends.
Formula
Charm = ∂Δ/∂t (delta change per unit time)
Worked example
A 1-day-to-expiry SPX 5,000 call has delta 0.50 with spot at 5,000. Tomorrow morning (T = 0), if spot is still 5,000, that delta is either 1 (if it expires ITM by 1 cent) or 0 (if OTM) — a massive overnight delta change. Charm doesn't just describe gradual decay; it captures the cliff. Dealers hedging this call book a meaningful charm rebalance through Thursday and Friday, contributing to the well-known monthly opex price action.
Related concepts
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