Delta (Δ)
Delta is the first-order sensitivity of an option's value to the spot price. For a BSM call: Δ = e^(−δT)·N(d₁) ∈ [0, 1]. For a put: Δ = −e^(−δT)·N(−d₁) ∈ [−1, 0]. An ATM call has Δ ≈ 0.5, deep ITM approaches 1, deep OTM approaches 0. Delta is also interpreted as the replication ratio: buying Δ shares per call creates a delta-neutral hedge. Delta changes over time (it is not constant), which is why dynamic hedging (delta rebalancing) is necessary. Delta also approximates the probability that the option expires in-the-money under the risk-neutral measure.
Related Terms
Black-Scholes-Merton Model (BSM)
The foundational option pricing formula that gives the fair value of a European call or put as a function of spot, strike, rate, volatility, and time.
Gamma (Γ)
The rate of change of delta with respect to the spot price — the curvature of the option's value.
Vega (ν)
The sensitivity of an option's price to a 1% change in implied volatility.
Theta (Θ)
The rate at which an option loses value as time passes — time decay per calendar day.
Delta-Neutral Portfolio
A portfolio whose value is insensitive to small moves in the underlying — achieved by balancing positive and negative deltas.
Put-Call Parity
The no-arbitrage relationship between European call and put prices: C − P = S·e^(−δT) − K·e^(−rT).