Enter spot, strike, days to expiry and implied volatility. The theoretical price of the option and its Greeks then follow. Two of those Greeks are delta and gamma. The other three are theta, vega and rho.
These numbers come from the Black-Scholes model, not from a market price. The whole computation happens in your browser.
Your numbers
Theoretical result
- Theoretical keemat (₹)
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- Implied volatility (%)
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- Delta
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- Gamma
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- Theta (per day)
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- Vega (per 1% IV)
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- Rho (per 1% rate)
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- d1
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- d2
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What the Greeks mean
- Delta
- Delta states how much the theoretical price of the option changes for a ₹1 change in spot.
- Gamma
- Gamma states how much delta itself changes for a ₹1 change in spot.
- Theta
- Theta states how much the theoretical price of the option changes as one day passes, everything else staying the same.
- Vega
- Vega states how much the theoretical price of the option changes for a 1 percentage point change in implied volatility.
- Rho
- Rho states how much the theoretical price of the option changes for a 1 percentage point change in the risk-free rate.
Quick Answers
- Which option greeks does this calculator compute?
- Two are Delta and Gamma. The other three are Theta, Vega and Rho. All 5 come from the Black-Scholes model, along with the option price for the inputs you enter.
- What inputs does the Black-Scholes model need?
- Spot price and strike are 2 of the inputs. Time to expiry in days and volatility make 2 more. The risk-free rate is the 5th. Every greek on this page comes from that same set.
The Black-Scholes Formula
T = days ÷ 365. d1 = [ln(spot ÷ strike) + (r − q + σ² ÷ 2) × T] ÷ (σ × √T), and d2 = d1 − σ × √T. Here σ is implied volatility, r the risk-free rate and q the dividend yield.
Call = spot × e^(−q×T) × N(d1) − strike × e^(−r×T) × N(d2). Put = strike × e^(−r×T) × N(−d2) − spot × e^(−q×T) × N(−d1). N(x) is the standard normal distribution function.
This Is a Model, Not a Measurement
Black-Scholes assumes certain things about the market. The option is exercised only at expiry, volatility stays constant throughout, and returns are lognormal. The market matches none of these exactly. So these numbers are the model’s answer, and nothing in them is a market price.
For N(x) this page uses the Abramowitz–Stegun polynomial approximation, whose maximum error is 7.5 × 10⁻⁸. These numbers are a computation, and they are not investment advice of any kind.
Related pages
Frequently Asked Questions
Why are these numbers called "theoretical"?
Because they come out of the Black-Scholes model, not out of a market price. The model assumes certain things: European exercise, constant volatility and no jumps. The market matches none of them exactly. So the number is the model’s answer, not the market’s.
What are d1 and d2?
They are two intermediate numbers in the Black-Scholes formula. D1 = [ln(spot ÷ strike) + (rate − dividend + IV² ÷ 2) × T] ÷ (IV × √T). D2 = D1 − IV × √T. T is the time to expiry in years.
Is theta per day or per year?
Per DAY. The formula gives theta on a yearly basis; on this page it is divided by 365. The difference is large. Yearly theta and daily theta for the same position can differ by a factor of a few hundred.
How is IV derived from a price?
There is no direct formula — there is no simple way back from a price to a volatility. This page halves the range from 0.1% to 500% again and again until the model price matches the price you entered. If no volatility in that range fits, the page states so instead of printing a number.
Why can days to expiry not be zero?
At zero days, IV × √T in the formula also becomes zero, and d1 has to be divided by it. In that case gamma and theta come out as infinity — which is not an answer. The model of expiry day itself is a different one.
What should be entered for the risk-free rate?
That is your own number. A starting value is filled in on this page and the field is editable. It is not a fixed or statutory rate — it moves with the market, and this page puts forward no number for it.
Are the numbers I enter sent anywhere?
No. The whole computation happens in your browser. No number goes to any server and nothing is saved anywhere.