Black-Scholes Calculator
European option prices and Greeks.
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This Black-Scholes calculator prices European call and put options using the Black-Scholes-Merton model. Enter the underlying price, strike price, days to expiry, implied volatility, risk-free rate and dividend yield to get the theoretical option prices and the Greeks: delta, gamma, theta, vega and rho.
What is a Black-Scholes Calculator?
The Black-Scholes-Merton model, published in 1973, gives a theoretical price for European options, which can be exercised only at expiry. It uses five inputs, the underlying price, strike, time to expiry, volatility and the risk-free rate, plus a dividend yield in the Merton version.
The model also gives the Greeks, which measure how the option price changes: delta (price), gamma (delta’s change), theta (time decay), vega (volatility) and rho (interest rates). Traders use them to manage risk. This Black-Scholes calculator returns prices and Greeks for both calls and puts.
How does the Black-Scholes Calculator work?
The calculator computes d1 and d2 from the inputs, then uses the standard normal distribution to price the call and put. The Greeks come from the model’s partial derivatives. Theta is shown per calendar day, vega per one percentage point of volatility and rho per one percentage point of interest rate.
How to use the Black-Scholes Calculator step by step
- Choose your currency.
- Enter the underlying price and strike.
- Enter days to expiry.
- Enter implied volatility.
- Enter the risk-free rate and dividend yield.
- Read the prices and Greeks.
Black-Scholes Calculator example with real numbers
A stock trades at $100. You want the fair value of a call and a put with a $105 strike expiring in 30 days, using 25% implied volatility and a 5% risk-free rate.
| Example input | Value |
|---|---|
| Currency | US dollar ($) |
| Underlying price | 100 |
| Strike price | 105 |
| Days to expiry | 30 days |
| Implied volatility (yearly) | 25% |
| Risk-free interest rate | 5% |
| Dividend yield | 0% |
| Example output | Value |
|---|---|
| Call option value | $1.19 |
| d1 | -0.5876 |
| d2 | -0.6592 |
| Probability call ends in the money (N(d2)) | 25.5% |
| Intrinsic value (call / put) | $0.00 / $5.00 |
| Put-call parity check (should be 0) | $0.000000 |
The Black-Scholes calculator values the call at $1.19 and shows Put option value $5.76. The call has about a 25.5% chance of finishing in the money.
Key features of this Black-Scholes Calculator
- Call and put prices
- Delta, gamma, theta, vega, rho
- Dividend yield (Merton)
- Probability in the money
- Put-call parity check
Who should use the Black-Scholes Calculator?
Who is this Black-Scholes Calculator for?
- Options traders
- Finance and FRM students
- Risk managers
- Nifty and Bank Nifty option traders
Practical use cases
- Checking if an option looks cheap or expensive
- Estimating time decay
- Learning the Greeks
- Comparing strikes and expiries
Key benefits
- Complete: prices and all Greeks.
- Accurate: standard model.
- Fast: live results.
- Private: runs in your browser.
Tips for better results
- Use implied volatility from the option chain, not historical volatility.
- Theta accelerates close to expiry.
- Compare the model price with the market bid and ask.
- Use a rate matching the option’s life, such as a T-bill yield.
Common mistakes to avoid
- Entering volatility as a decimal instead of a percentage.
- Using it for American options with early exercise value.
- Ignoring dividends.
- Treating the model price as a guaranteed fair price.
Limitations of this Black-Scholes Calculator
- European options only.
- Constant volatility and rates.
- No transaction costs or early exercise.
Black-Scholes Calculator vs other ways to calculate
| Greek | Measures |
|---|---|
| Delta | Change in option price per 1 change in underlying |
| Gamma | Change in delta |
| Theta | Daily time decay |
| Vega | Change per 1% volatility |
| Rho | Change per 1% interest rate |
To see profit at expiry, use the options profit calculator. To size a trade, try the risk reward calculator.
Privacy and data handling
This Black-Scholes Calculator runs entirely in your browser. The numbers you type are not sent to Qorico or stored on any server, and nothing is saved after you close the page. The Copy and Download buttons create the result on your own device. If the page has analytics turned on, it may count that a calculation happened, but it does not record the values you entered.
Black-Scholes Calculator FAQs
What is the Black-Scholes model?
A formula for the theoretical price of European options, based on price, strike, time, volatility and interest rates.
What are the option Greeks?
Measures of how an option’s price changes with the underlying price, time, volatility and interest rates.
Does Black-Scholes work for American options?
Not exactly; it ignores early exercise, which matters mostly for puts and dividend-paying stocks.
Which volatility should I use?
Implied volatility from the market’s option prices.
Can I use it for Nifty options?
Yes. NSE index options are European-style; choose INR and use the index level and India’s risk-free rate.
Why does my broker's price differ?
Markets price in volatility smiles, supply and demand and fees.
Related tools
Sources and references
We checked the method and the current figures used in this Black-Scholes Calculator against these official and primary sources:
- Options Industry Council: Options education
- Cboe: Options education
- SEBI Investor Website
- National Stock Exchange of India
Written and reviewed by the Qorico Team
