Derivatives · Core
Delta
Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.
Definition
Δ = ∂V/∂S. A 40-delta call behaves, locally, like 0.4 shares. Spot delta and forward delta differ when there is carry. Digital and barrier products have deltas that jump.
Why it matters
Dealer hedging flow is delta. A street that is short gamma buys as the market rises — the familiar chase.
Case
0DTE call walls: as spot rises, dealer short-gamma hedging buys futures. Delta was the transmission, not the news.
How to read it
State spot vs forward delta and the hedge instrument. A 25-delta put is a product name, not just a Greek.
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