Option Price Calculator (Black-Scholes)
Theoretical call and put prices with delta, gamma, theta, vega and rho, plus implied volatility from a market premium, with Nifty and Bank Nifty one click away.
The Black-Scholes model prices an option from the spot price, strike, days to expiry, implied volatility and interest rate, and gives its Greeks: delta, gamma, theta, vega and rho. Enter any option, or load Nifty's or Bank Nifty's at-the-money option from the latest chain, and back out implied volatility from a market premium.
An option's premium is its intrinsic value plus time value, and the time value depends on how far the underlying might move before expiry. The Black-Scholes model turns that into a price using the implied volatility, and its sensitivities (the Greeks) show how the price changes when the spot, time, volatility or rate move.
Index options on NSE and BSE, and stock options on NSE, are European-style (exercised only at expiry), which is the case Black-Scholes is built for. Load the latest at-the-money Nifty or Bank Nifty option to start from real numbers, then change any input.
The Black-Scholes formula
d1 = [ln(S / K) + (r − q + σ² / 2) T] / (σ √T), d2 = d1 − σ √T. Call = S e−qT N(d1) − K e−rT N(d2); put = K e−rT N(−d2) − S e−qT N(−d1). S is the spot, K the strike, T the time to expiry in years (days / 365), r the interest rate, q the dividend yield, σ the volatility and N the standard normal distribution.
The default rate is the one Strota's option chains use for their Greeks. For index options, a dividend yield of zero is the usual simplification; for a stock with a dividend due before expiry, entering its yield lowers the call price and raises the put.
What the Greeks mean
Delta: the change in premium for a ₹1 move in the underlying, roughly 0.5 at the money. Gamma: how much delta changes per ₹1 move; it peaks at the money near expiry. Theta: premium lost per calendar day with nothing else changing. Vega: the change for one percentage point of implied volatility. Rho: the change for one percentage point of interest rate, small for short-dated options.
The Nifty option Greeks page shows these for every strike of the current Nifty and Bank Nifty chains.
Implied volatility
Volatility is the one input the market does not quote directly. Given a market premium, the calculator finds the volatility at which the model price matches it: that is the option's implied volatility. A premium below the option's minimum value has no implied volatility. The India VIX is a volatility index built from Nifty option prices in a similar spirit.
Key takeaways
- Black-Scholes prices European options, which is what NSE and BSE index and stock options are.
- Theta here is per calendar day; vega and rho are per one percentage point.
- Implied volatility is the volatility at which the model price equals the market premium.
- The model's probability of expiring in the money is a risk-neutral figure, not a forecast.
Frequently asked questions
How is an option price calculated?
With the Black-Scholes model: from the spot price, strike, time to expiry, implied volatility, interest rate and dividend yield. The premium is intrinsic value (how far in the money the option is) plus time value, which grows with volatility and time left.
How do I calculate implied volatility?
Enter the option's market premium with its spot, strike, days to expiry and rate. Implied volatility is the volatility that makes the Black-Scholes price equal that premium; it has no formula, so the calculator searches for it numerically.
What interest rate should I use for Nifty options?
A short-term rupee rate. The calculator defaults to the rate Strota's option chains use; for weekly options the rate barely changes the price, while for longer-dated options it matters more.
Why does the calculator's price differ from the market price?
The model price is only as good as the volatility you enter. Each strike trades at its own implied volatility (the volatility smile), and quoted prices can be stale or wide. Enter the market premium in the implied volatility box to get the volatility the market is actually using.
Is the Black-Scholes model valid for Indian options?
Indian index and stock options are European-style and cash-settled for indices, which fits the model's main assumption. Its assumption of constant volatility does not hold, which is why implied volatility differs by strike.