Free tools · Options
Black-Scholes calculator — option fair value and Greeks
Last updated:
Short answer
The Black-Scholes model prices a European option from five inputs — spot price, strike, time to expiry, implied volatility and the risk-free rate — and its derivatives give the Greeks: Delta (directional exposure), Gamma (how fast Delta changes), Theta (daily time decay), Vega (sensitivity to a 1% IV change) and Rho (rate sensitivity). NSE index and stock options are European-style, so the model applies directly. Enter your option below to get fair value and all five Greeks instantly.
Delta
—
per 1-pt move in spot
Gamma
—
Delta change per 1 pt
Theta
—
per calendar day
Vega
—
per 1% IV change
Rho
—
per 1% rate change
European-style pricing (all NSE options are European). Theta is shown per calendar day; Vega and Rho per one-percentage-point change. Enter the option chain’s IV to reproduce market prices, or your own volatility estimate to compare against them.
Reference: at-the-money call fair value by IV and days to expiry
Spot = strike = ₹25,000, risk-free rate 6.5%. Same model as the calculator; a put at the money is worth slightly less by the carry on the strike.
| Implied volatility | 7 days | 15 days | 30 days | 60 days |
|---|---|---|---|---|
| 12% | ₹181.68 | ₹277.10 | ₹412.91 | ₹627.06 |
| 15% | ₹222.99 | ₹337.37 | ₹497.62 | ₹745.37 |
| 20% | ₹291.91 | ₹438.03 | ₹639.34 | ₹944.04 |
| 25% | ₹360.86 | ₹538.78 | ₹781.36 | ₹1,143.55 |
Every option chain quote is the market’s answer to the same equation this calculator runs. Black-Scholes will not tell you whether NIFTY rises — it tells you what a given view of volatility and time is worth, which is the arithmetic every serious options trade rests on: whether the straddle you are selling is rich, how much Theta you collect per day, how hard a 1% IV crush hits your position.
All NSE options — index and stock alike — are European-style (exercisable only at expiry), which is precisely the case Black-Scholes models. Enter spot, strike, days to expiry and implied volatility; the tool returns fair value and the full Greek panel, for calls and puts.
The five inputs, and where to find them
Spot is the current index or stock price. Strike is the option’s exercise price. Time to expiry is calendar days until the contract expires — the calculator converts to years internally. Implied volatility is the market’s expected annualised volatility, published per-strike on the NSE option chain; using the chain’s IV reproduces the market price, while using your own volatility estimate reveals whether you think the option is cheap or dear. The risk-free rate is conventionally taken from short-term government yields — a figure in the 6–7% region is typical for India; the result is not very sensitive to it.
One honest caveat: Black-Scholes assumes constant volatility and no jumps, which real markets violate — that is why different strikes trade at different IVs (the “smile”). The model remains the industry’s common language for quoting and hedging, but treat its output as a consistent reference, not gospel truth.
Reading the Greeks
Delta is the option’s price change per one-point move in the underlying — 0.5 for an at-the-money call, approaching 1 deep in the money, 0 far out. It doubles as a rough market-implied probability of expiring in the money. Gamma is Delta’s rate of change: highest at the money near expiry, which is why expiry-day option prices whip around so violently. Theta is the value lost per day from time decay — the income of sellers and the rent buyers pay; it accelerates as expiry approaches.
Vega is the price change per one-percentage-point move in IV. It is largest for at-the-money options with time remaining — which is why buying options before a known event is expensive and why IV crush after the event hurts holders even when direction was right. Rho, the sensitivity to interest rates, is the least consequential for short-dated Indian index options but is included for completeness.
Strategies live and die on Greeks in combination: a short straddle is short Vega and long Theta but dangerously short Gamma; a long call is long Delta and Vega but bleeds Theta daily. If you can read the panel this calculator produces, you can state precisely what has to happen for a trade to make money — before putting it on.
From pricing an option to testing a strategy
A Greeks panel prices one moment; a strategy is thousands of such moments chained across years of market regimes. Whether systematically selling strangles or buying breakout calls actually made money on NIFTY — after Theta, after IV cycles, after the full Indian cost stack of brokerage, STT on premium, exchange charges and slippage — is an empirical question, and backtesting is how it gets answered.
INDfolio AI backtests options strategies on NSE history with strike selection, lot sizes, expiry handling and per-leg costs modelled honestly — the same rigour this calculator applies to a single option, extended to an entire system. Describe the strategy in plain English; the data judges it.
These calculators are free, run entirely in your browser, and store nothing. They produce estimates for NSE trades based on published rates and standard formulas — not investment advice, and not a substitute for your broker’s contract note. INDfolio AI builds algo trading software; the honest connection is that our backtests apply this same cost arithmetic to every simulated trade.