Calculator
Black-Scholes option calculator
The model's fair premium and all five Greeks — delta, gamma, vega, theta and rho — from six inputs.
Premium is model output, not a quote — feed the live option chain's IV for a usable number.
Call · ATM
₹23.3
₹23,300 per 1000-share lot · breakeven ₹1,023.3 · 42.91× gearing
Hover a segment for value + share.
- Delta₹ move in premium per ₹1 move in the underlying0.5515
- GammaHow fast delta itself moves0.007666
- VegaPremium change per 1 vol point1.1342
- ThetaPremium decay per calendar day-0.4343
- RhoPremium change per 1 rate point0.4341
What this calculator answers
With spot at 1,000, a 1,000 strike, 30 days to expiry, 18% implied volatility and a 6.5% risk-free rate, the model's call premium comes out around ₹54 with a delta near 0.55 — so a ₹1 move in the underlying is worth about ₹0.55 of premium. The premium is only as good as the volatility you feed it: put the chain's live IV in, not a round number.
How it is calculated
Black-Scholes with a continuous dividend yield. d1 and d2 come from spot, strike, time to expiry, rate, dividend yield and volatility; the normal CDF is the Abramowitz & Stegun approximation. Delta is the discounted CDF term, gamma the density over spot times volatility, vega the premium per one volatility point, theta the calendar-day decay including financing, and rho the premium per one rate point.
European exercise, continuous dividend yield, no bid-ask spread and no early-exercise premium. Real NSE and BSE options are American-style with weekly expiries, and the market price also carries a volatility smile — the model is a fair-value reference, not a quote.
Common questions
Which Greek matters most for a buyer?
Delta and theta. Delta says how much of the move you actually capture; theta is the daily cost of waiting. For a seller the two that hurt are gamma (delta moves faster against you near the strike) and vega (a volatility rise lifts the premium you must buy back).
Why is my premium different from the exchange price?
Almost always the volatility. Market IV differs from the historical volatility the model assumes, and it is not flat across strikes — the smile means out-of-the-money options carry a higher IV than at-the-money ones. Feed the chain's IV for that strike and expiry.
Does the model predict the direction?
No. It prices what an option is worth given the inputs, assuming you are not forecasting the direction. A model premium well below the market price is usually a warning about your volatility assumption, not a free trade.
Source & freshness
- Source
- Deterministic formula in lib/calculators.ts
- Timeliness
- Static-verified
- Method
- calculated
- Note
- Illustrative projection from your inputs — not a market quote.