Option Greeks Calculator (Delta, Gamma, Vega, Theta, Rho, Vanna & Volga)
All the Black-Scholes Greeks for a call and put at once — delta, gamma, vega per IV point, theta per day, rho per rate point, plus vanna and volga (vomma) — with dividend yield, the dollar Greeks for a position of N contracts, a one-day / one-percent scenario P&L, and a table of how the Greeks change across the strike.
How it works
Δ_call = e^(−qT) N(d₁), Δ_put = e^(−qT)[N(d₁) − 1] · Γ = e^(−qT) φ(d₁) ÷ (S σ √T) · vega = S e^(−qT) φ(d₁) √T (÷ 100 per IV point) · θ_call = −S e^(−qT) φ(d₁) σ ÷ (2√T) − r K e^(−rT) N(d₂) + q S e^(−qT) N(d₁) (÷ 365 per day) · ρ_call = K T e^(−rT) N(d₂) (÷ 100 per point) · vanna = −e^(−qT) φ(d₁) d₂ ÷ σ · volga = vega × d₁ d₂ ÷ σ
The Greeks are the partial derivatives of an option's model price — how much it moves per dollar of the underlying (delta), how fast that sensitivity itself changes (gamma), per point of implied volatility (vega), per day (theta) and per point of interest rate (rho) — and they are what a trader actually manages, because a book of options is hedged Greek by Greek rather than option by option. Multiplied by contracts and multiplier they become dollar exposures, and combined into a scenario they show the asymmetry that defines options: long gamma gains on moves in either direction while theta bleeds every day, and the balance between the two is the whole trade.
Worked example
A 30-day at-the-money call on a $100 stock at 25% volatility and a 4.5% rate is worth about $3.04 with delta 0.53, gamma 0.055, vega $0.114 per IV point and theta about −$0.054 a day. Ten contracts carry 535 shares of delta, $114 of vega and lose about $54 a day; a 1% rally earns roughly $535 of delta plus $28 of gamma ($563), and a 1% drop loses about $507 — the gamma cushion that the theta pays for.
Frequently asked questions
Why does my broker show different Greeks?
Brokers use the live implied volatility per strike, actual days including weekends or trading days only, a different rate or dividend schedule, and sometimes an American-option model. Differences of a few percent are normal; the shape and relative sizes will match.
Is delta the probability of expiring in the money?
Roughly, for near-the-money options: N(d₂) is the risk-neutral probability and delta is N(d₁), slightly larger. The gap grows with volatility and time — a 0.30-delta call might have a 26% chance of finishing in the money.
Related calculators
Educational finance mathematics. Models such as Black-Scholes, parametric VaR and lognormal Monte Carlo rest on simplifying assumptions (constant volatility, normal returns, no fat tails) that real markets violate. Nothing here is investment advice — consult a licensed professional for decisions about your money.