Black-Scholes option calculator
Pick a stock and price a European call and put with all the Greeks — the price, volatility, dividend and interest rate fill themselves in.
| Greek | Call | Put | What it says |
|---|---|---|---|
| Delta | 0.275 | -0.725 | How much the option moves when the stock moves by 1. |
| Gamma | 0.0465 | 0.0465 | How much delta itself changes per 1 move in the stock (how fast it "accelerates"). |
| Vega | 0.096 | 0.096 | Price change when volatility rises by 1 percentage point. |
| Theta | -0.043 | -0.031 | How much the option loses each day just from time passing ⏳. |
| Rho | 0.022 | -0.064 | Price change when interest rates rise by 1 percentage point. |
d1 = -0.5990 · d2 = -0.6707
In plain words 💡
A call option is the right, not the obligation, to buy a stock at the strike price on expiry day. A put is the right to sell it. Black-Scholes answers one question: what is that right worth today, if the stock price wanders randomly with a given volatility.
Volatility does most of the work 🎢: the more the stock can swing, the more the right is worth, because an option's upside is open-ended while the loss stops at the price paid. Time works the other way — every day eats a little of the value (theta).
Where the formula is wrong ⚠️
It assumes constant volatility, continuous trading and no price jumps. With a ticker picked we use last year's historical volatility, while the market prices options with implied volatility — a different one for every strike (the volatility smile). So the result is a textbook price, not an exchange quote. The model is for European options (exercise only on expiry day).
Read more 📚
An educational tool: it runs a formula on historical data or on the numbers you type. It is not a forecast or a recommendation, and it knows nothing about your situation.