Options Greeks
Calculator
Delta, gamma, theta, vega and rho for any NSE call or put — computed with Black-Scholes from spot, strike, days to expiry, IV and the risk-free rate.
Inputs
Greeks
European-style, no dividends. Theta is annual ÷ 365; vega and rho are per one percentage-point.
How it's calculated
This uses the Black-Scholes model. First it converts the inputs: time t = days ÷ 365, volatility v and rate r are expressed as decimals. Then it computes the two standard terms:
- d1 = ( ln(S ÷ K) + (r + v² ÷ 2) · t ) ÷ ( v · √t )
- d2 = d1 − v · √t
where S is spot and K is strike. N() is the standard normal cumulative distribution (here the Abramowitz-Stegun approximation) and n() is the normal probability density. From these come the Greeks:
- Delta: call = N(d1); put = N(d1) − 1. How much the option price moves per ₹1 of spot.
- Gamma: n(d1) ÷ (S · v · √t). The rate of change of delta — same for calls and puts.
- Theta (per day): the annual Black-Scholes theta divided by 365 — the daily cost of time decay in rupees.
- Vega (per 1% IV): S · n(d1) · √t ÷ 100 — the price change for a one-point move in implied volatility.
- Rho (per 1% rate): the rate sensitivity divided by 100 — the price change for a one-point move in interest rates.
If days, IV, spot or strike is zero or blank the option has no time value, so the calculator falls back to intrinsic-only behaviour (delta 0 or ±1, all other Greeks 0) rather than showing errors.
FAQ
What are the option Greeks?
They measure how an option's price reacts to its drivers — delta to the spot price, gamma to the change in delta, theta to the passage of time, vega to implied volatility and rho to interest rates. Together they describe the risk of a position far better than the premium alone.
Why is theta shown per day?
The raw Black-Scholes theta is an annual figure. Dividing by 365 gives the rupee value the option is expected to lose each calendar day to time decay, all else equal — the number traders actually watch.
Why is vega quoted per 1% of IV?
The textbook vega is per one whole unit (100%) of volatility, which is unwieldy. Dividing by 100 gives the price move for each one percentage-point change in IV, matching how IV is quoted on the chain.
Live Greeks on the option chain
TradePulse shows live delta, gamma, theta, vega and IV across every strike for NSE F&O — free to start.