Delta-Neutral Portfolio
A portfolio whose value is insensitive to small moves in the underlying — achieved by balancing positive and negative deltas.
A delta-neutral position has ΔPortfolio = 0. For a single short call (Δ = −0.6), the hedge ratio is: buy 0.6 shares per short call. Delta neutrality is maintained dynamically: as the stock price changes, delta changes (due to gamma), requiring rebalancing. The P&L of a delta-neutral, gamma-positive position is: P&L ≈ ½Γ(ΔS)² − Θ·Δt. Delta-neutral strategies isolate volatility exposure (gamma/vega) from directional exposure.
Delta (Δ)
The sensitivity of an option's price to a $1 change in the underlying spot price.
Gamma (Γ)
The rate of change of delta with respect to the spot price — the curvature of the option's value.
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.
Theta (Θ)
The rate at which an option loses value as time passes — time decay per calendar day.
Vega (ν)
The sensitivity of an option's price to a 1% change in implied volatility.
Rho (ρ)
The sensitivity of an option's price to a 1% change in the risk-free interest rate.