What is Options Greeks?
The Options Greeks are sensitivity measures that quantify how an option's price changes in response to movements in the underlying stock, time, volatility, and interest rates. Delta (Δ) measures price sensitivity to the stock; Gamma (Γ) is the rate of change of Delta; Theta (Θ) measures time decay per day; Vega (V) measures sensitivity to implied volatility; Rho (ρ) measures sensitivity to interest rates. Together they form a complete risk picture for any options position. Professional traders continuously monitor Greek exposures at the portfolio level to maintain their desired risk profile and hedge unwanted exposures. This calculator uses the Black-Scholes model to compute all five Greeks.
Formula
Delta (Δ) = N(d₁) for calls; N(d₁) − 1 for puts
Gamma (Γ) = φ(d₁) / (S × σ × √T)
Theta (Θ) = [−S × φ(d₁) × σ / (2√T) − r × K × e^(−rT) × N(d₂)] / 365
Vega (V) = S × φ(d₁) × √T / 100
Rho (ρ) = K × T × e^(−rT) × N(d₂) / 100 (calls)
φ(d₁) = standard normal PDF at d₁
N(·) = cumulative standard normal CDF
Same d₁, d₂ as Black-Scholes
Calculator
How to Use
- 1Enter the five BS inputs: Stock price, strike, days to expiry, risk-free rate (%), and implied volatility (%).
- 2Read Delta: For a call, Delta ranges 0-1. An ATM call has Delta ≈ 0.50. It also approximates the probability of expiring in-the-money.
- 3Monitor Theta: Theta is negative for long options: you lose this amount in time value per calendar day, accelerating near expiry.
- 4Watch Vega for earnings: High Vega means the option is very sensitive to IV changes. Long options before earnings benefit from IV expansion; short options are hurt.
Worked Example
Example: 30-day ATM call, IV=25%
S
$150
K
$150
DTE
30
Rate
5%
IV
25%
Delta ≈ 0.52, Gamma ≈ 0.054, Theta ≈ −$0.08/day, Vega ≈ $0.30 per 1% IV move. The option decays 8 cents per day and gains 30 cents for every 1 percentage point increase in implied volatility.