What the calculator computes
Six inputs, two prices and five Greeks. You enter the spot price of the underlying, the strike price of the option, the time to expiry (in days, which the page converts to years), the volatility of the underlying (annualised, in per cent), the interest rate (the model's r, in per cent), and a dividend figure for the underlying. The page returns the call and the put premium that the Black-Scholes-Merton equations give on those inputs.
The same page also returns the Greeks: Delta (how the option price moves per unit move in the spot), Gamma (how Delta moves per unit move in the spot), Theta per day (how the option price changes for a one-calendar-day passage), Vega per 1 point of volatility (how the price changes when annual volatility moves by one percentage point) and Rho per 1 point of the model's r. Intrinsic value and time value are split out next to the price, and a put-call parity check confirms that call minus put equals spot minus strike times e to the minus r times T.
Why this is a model, not a market price
Black-Scholes-Merton assumes constant volatility, continuous trading, no transaction costs, no early exercise and lognormal returns. Markets do not. The number the calculator shows is a theoretical value given your inputs, not the price at which you can trade. The market premium on an actual option often differs from the theoretical value because traders price in a different volatility (see implied volatility below) or because supply and demand pull the premium away from the model for short periods. Use the calculator to understand the sensitivities, not to decide what a contract is worth.
European style and how Indian options settle
Indian index options (Nifty 50, Bank Nifty, FinNifty, Sensex and similar indices) are European-style. European-style means the option can only be exercised on its expiry day, which is the input the calculator asks for. On the final settlement day, index options are cash-settled: the settlement reference is the closing level of the underlying index, and the difference between that level and the strike (adjusted for direction) is paid in cash. There is no delivery of index units because an index is not deliverable.
Single-stock options are also European-style, but they are physically settled: an open position at expiry results in delivery of the underlying shares in the demat account, not a cash payment. That means a stock option left to expire in the money can trigger a shares delivery you were not planning for, with full value payable.
The calculator uses the European-style formula, so it adds no value for early exercise.
The interest rate input (the model's r)
The model's r represents the time value of money over the life of the option. A common convention among Indian options texts is the cut-off yield from the RBI's weekly 91-day Treasury-bill auction. The page's default is 5.5 per cent, labelled user-editable. As of early November 2026, the 91-day Treasury-bill cut-off has traded in the 5.2 to 5.6 per cent range in RBI's weekly auctions (readings in July, August and September 2026 fell in that band). Update the input to the current auction cut-off for a cleaner answer.
Rate assumptions are one reason implied volatility differs between screens: two tools solving the same premium with different values of r will return different volatilities. This page states the input, the reference and the source, and leaves the number editable.
Why two calculators disagree on the same contract
Even with the same six inputs, two implementations will disagree slightly because of rounding, the day-count convention (365-day year versus 252-day trading-year), whether volatility is annualised from daily or weekly returns, whether the model's r is continuously or discretely compounded, and whether the model is Black-Scholes-Merton or Black-76 (which prices options on futures and takes a futures price rather than spot as an input). Black-76 is a different model, not a wrong one. This widget is Black-Scholes-Merton on spot, with a continuously compounded r and a 365-day year.
Worked example (checkable with a pocket calculator)
Sample inputs (not market data): spot 100, strike 100, 30 days to expiry, volatility 20 per cent, interest rate (the model's r) 5.5 per cent, no dividend. On these inputs the calculator gives a call premium of 2.51 and a put premium of 2.06.
- Intrinsic and time value. Intrinsic value for a call is max(spot minus strike, 0), and for a put is max(strike minus spot, 0). Here both are zero because the strike equals the spot. So the full call premium of 2.51 and the full put premium of 2.06 are time value.
- Put-call parity check. For a European option with no dividend, call minus put must equal spot minus strike times e to the minus r times T. T is 30 divided by 365, which is 0.0822 years. Minus r times T is minus 0.055 times 0.0822, which is minus 0.00452. e to the minus 0.00452 is 0.99549. Strike times that is 99.549. Spot minus 99.549 is 0.451. Call minus put is 2.51 minus 2.06, which is 0.45. Both sides agree to two decimals, so the premium output is internally consistent.
- A quick Greek read. For an at-the-money call at these inputs, Delta is close to 0.54 and the put Delta is about minus 0.46; Theta per day for the call is about minus 0.05 (the call loses about 0.05 per unit per calendar day if the other inputs hold); Vega per 1 point of annual volatility is about 0.11 (a one-point volatility rise lifts the premium by about 0.11). The widget shows exact values on your inputs.
The Greeks at a glance
| Greek | Measures | Sign call | Sign put | Unit the widget shows |
|---|---|---|---|---|
| Delta | Price change per 1-unit move in spot | Positive, 0 to 1 | Negative, minus 1 to 0 | Per 1 unit of underlying price |
| Gamma | Delta change per 1-unit move in spot | Positive | Positive | Per 1 unit of underlying price |
| Theta | Price change for one more day passed | Negative | Negative | Per calendar day |
| Vega | Price change per 1 percentage point of volatility | Positive | Positive | Per 1 point of annual volatility |
| Rho | Price change per 1 percentage point of r | Positive | Negative | Per 1 point of r |
Payoff at expiry versus theoretical value today
The widget shows two curves on the same axis. The payoff at expiry is the hard, piecewise-linear line a European option pays on expiry day: for a call, zero below the strike and spot minus strike above it; for a put, strike minus spot below the strike and zero above it. The theoretical value today is the Black-Scholes curve for the premium right now at each spot level, a smooth line that usually sits above the payoff by the amount of time value. A deep in-the-money European put can sit slightly below it, because the strike is received later. As expiry nears, the smooth curve collapses onto the kinked payoff.
Time decay curve
Holding all other inputs constant, the premium of an at-the-money option falls over time, slowly at first and faster as expiry approaches. The widget plots premium against days remaining so this shape is visible. Theta is not constant; it is steepest in the last few days.
Implied volatility from a market premium
Turn the model around: feed in the market premium of an option, and solve for the volatility input that would make the model print exactly that premium. This is implied volatility. The widget solves for it numerically. Implied volatility is one number per contract per moment, but it varies across strikes (the volatility smile) and across expiries (the term structure), which is why different options on the same underlying can show different implied volatilities at the same instant.
What this calculator is not
- It is not a quote source. The numbers you type stand in for live data; the calculator does not pull them from an exchange.
- It does not state current lot sizes, index levels or expiry weekdays, because those are set by the exchange and change (exchanges have reorganised weekly expiries in recent years). Check the contract specification on the exchange website for your trade.
- It does not include a margin, STT or brokerage figure in the premium. Trade economics (STT, brokerage, exchange charges, GST, SEBI charges, stamp duty) are on the brokerage calculator.
Frequently asked questions
Which model does the calculator use?
Black-Scholes-Merton for a European option on the spot price, with continuous compounding on r and a 365-day year. Black-76, which prices from a futures price rather than spot, would take different inputs and can give different outputs.
Why does the premium here differ from my broker's quote?
Markets quote at an implied volatility that moves tick by tick; this calculator shows what the model gives at the volatility you entered. Feed the market premium back into the implied-volatility solver and the volatility that comes out is the market's current reading.
Are Indian index options European or American?
European. Nifty 50, Bank Nifty, FinNifty and Sensex index options can only be exercised on expiry day. Their final settlement is in cash at the closing index level. Single-stock options are also European but physically settled, which means delivery of shares on expiry.
What should I put in for the interest rate?
A common convention is the RBI 91-day Treasury-bill cut-off yield from the weekly auction. The default of 5.5 per cent is user-editable. Replace it with the latest cut-off from RBI press releases for a cleaner answer.
What volatility should I type?
Annualised historical volatility of the underlying, in per cent. A rolling 20- or 30-day historical volatility is a common starting point. If you have a market premium, let the implied-volatility solver give you the number the market is using.
Why is Theta expressed per day?
Because that is the number traders read directly. The model's Theta is strictly per unit of time; most Indian trading screens convert it to per calendar day for readability, which is what this page does. Theta per trading day is a different conversion; the value will be larger by about 365 divided by 252.
Does the calculator work with weekly options?
Yes. Weekly options are standard Black-Scholes-Merton inputs with a short time-to-expiry. Enter the days remaining, keep every other input the same, and the output is correct. The Greeks move faster on short-dated options, which the output will reflect.
Is the implied-volatility solver deterministic?
Yes. The same market premium and the same other inputs give the same implied volatility every time, within the solver's tolerance. If the premium you enter falls below the intrinsic value or above the no-arbitrage bound, the solver flags an unreachable premium rather than return a number.
Courses that teach the subject behind the option pricing calculator
Option Greeks Trading Course
NIFM says this course will elevate your options education and covers Delta, Gamma, Vega, Theta and Rho across eight chapters. Duration is listed at seven hours, validity is six months, and the language is Hindi.
₹5,500 + 18% GST
Equity Derivative NISM Series VIII SEBI Certification Course
Index construction, forwards and futures, options pricing fundamentals, the Greeks, equity strategies, hedging with protective puts and covered calls, clearing and settlement, and the SEBI framework. Preparation for the NISM Series VIII certification exam.
₹2,500 + 18% GST
Option Trading Strategies Module
Payoff structures, strategy creation and risk management across 16 strategy chapters, including synthetic long call, covered call, straddle, strangle, collar, bull and bear spreads, butterfly, condor, call-put parity and ratio spreads.
₹2,500 + 18% GST
