Black-Scholes Option Pricing Calculator
Theoretical call and put prices with all five Greeks, from spot, strike, expiry, volatility and rates.
Result
- Moneyness
- At the money
- 30 days to expiry
- Call delta
- 0.5609
- Change in the call price for a ₹1 move in the underlying
- Put delta
- -0.4391
- Negative: a put gains when the underlying falls
- Gamma
- 0.000393
- Change in delta for a ₹1 move. Same for the call and the put
- Vega
- ₹28.26
- Gain per 1 percentage point rise in volatility. Same for the call and the put
- Call theta (per day)
- −₹9.01
- What one calendar day costs the holder, all else equal
- Put theta (per day)
- −₹4.58
- Call rho
- ₹11.14
- Change per 1 percentage point move in the interest rate
- Put rho
- −₹9.30
- d₁ / d₂
- 0.1532 / 0.1130
- N(d₂) is the risk-neutral probability the call finishes in the money
Black-Scholes prices a European option under constant volatility in a frictionless market. None of those assumptions holds exactly — a real option chain shows a different implied volatility at every strike. Every exchange-traded option in India, index and single-stock alike, is European-style, so the exercise rule fits the model; the volatility does not, so treat these as a reference value rather than a quote. This is arithmetic on the numbers you entered, not a price, a forecast or advice to trade.
Estimated from the numbers you entered — not a projection of guaranteed returns.
About this calculator
Black-Scholes turns six inputs into what an option is theoretically worth, and into the Greeks that describe how that value moves. It is the reference model the whole options market is quoted against — which is why implied volatility, the number traders actually watch, is defined as the volatility you would have to put into this formula to get the market price back out.
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)
- where S = spot, K = strike, T = years to expiry, σ = volatility, r = risk-free rate, q = dividend yield, and N is the standard normal CDF
Frequently asked questions
Does Black-Scholes work for Indian options?
On exercise, yes: every exchange-traded option in India is European-style, which is what the model prices. That covers index options such as NIFTY and BANKNIFTY and single-stock options alike, which NSE made European for contracts expiring from 27 January 2011; single-stock options also settle by delivery at expiry. Where the model falls short is volatility: it assumes one figure at every strike, and a real option chain does not show that. It remains the standard reference because implied volatility is defined against it.
Which volatility should I enter?
If you want the theoretical value the market is currently implying, enter the implied volatility shown against that strike on the option chain. If you want your own view of fair value, enter your estimate of how volatile the underlying will actually be until expiry. The two answer different questions.
Why is the calculated price different from the market price?
Almost always because the volatility you entered differs from what the market is implying at that strike. Work the other way round with the implied volatility calculator: put in the market price and it returns the volatility that reproduces it.
Should I use calendar days or trading days?
Calendar days. Time in the formula is wall-clock time to expiry, and a weekend still carries interest and still passes. Some desks make a trading-day adjustment for theta; this calculator does not.
What is theta actually telling me?
What one calendar day costs the option holder if nothing else changes. It is shown per day here rather than per year, because that is how it is read. Theta is not linear — it accelerates as expiry approaches, especially at the money.
Is a high Greek good or bad?
Neither. The Greeks are sensitivities, not scores. High gamma means the delta moves fast, which helps a buyer and hurts a seller. The sign of the position determines what a number means.