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Black-Scholes Option Pricing

The Nobel-winning formula that built the modern derivatives market. Price an option from five inputs and see how the Greeks measure its every sensitivity.

Black-Scholes Option PricingLive

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The Black-Scholes formula prices a European option from spot, strike, time, rate, and volatility. The Greeks measure sensitivity: delta to price, gamma to delta, vega to volatility, theta to time decay. Educational tool — not investment advice.

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Call price$8.01
Put price$6.03
Delta (call)0.580
Gamma0.0221
Vega (per 1%)0.276
Theta (per day)-0.024

Governing equation

Reading this result: Spot 100 vs strike 100 makes this call at-the-money (intrinsic value 0.00). A higher volatility σ (now 25%) and a longer time to expiry (now 0.50 yr) both raise the option's value by adding time value — more room for the underlying to finish favorably. As the option moves deeper in-the-money its delta approaches 1 and it behaves like the underlying itself.

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How it works

The Black-Scholes model gives the fair value of a European option from spot price, strike, time to expiry, risk-free rate, and volatility. The Greeks — delta, gamma, vega, theta, rho — quantify how that value responds to each input, and are the language of options hedging. This is an educational tool, not investment advice.

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Frequently asked questions

Is this Black-Scholes calculator tool really free?
Yes. Black-Scholes Option Pricing runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.