Delta
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
Δ = (partial V)/(partial S) — the share-equivalent hedge ratio. For a BSM call Δ_call = N(d_1) in (0,1); for a put Δ_put = N(d_1) - 1 in (-1,0). Approximately equal to the risk-neutral ITM probability for ATM options (delta-as-probability heuristic on the FX desk). Quoting convention varies by market: equities quote in dollars, FX in 'delta strikes' (25-delta risk reversal, 25-delta butterfly), rates in DV01.
Delta in plain English
Delta answers a simple question about an option: if the underlying stock moves by $1, how much does the option's value move? It's written Δ = partial V / partial S and acts as a 'how many shares am I effectively holding' number — a call's delta sits between 0 and 1, a put's between -1 and 0. It doubles as a rough gauge of the option's chance of finishing in-the-money, which is why traders casually treat a '25-delta' option as one with about a 25% shot. Different markets quote it differently — stocks in dollars, currencies by 'delta strikes', bonds via a related measure called DV01 — but the core idea is always the same sensitivity to the underlying's move.
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