Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Researchers · Black-Scholes

Black-Scholes for a hedge position

Built for researchers prototyping or validating an idea. Prototype fast, reproduce exactly, and share a citable, interactive version of your model. Simulate a hedge position live below — adjust the inputs and watch it respond, right in your browser.

Black-Scholes Option PricingLive

fair value + the Greeks

Controls

Presets

Spot price S

Strike K

Time to expiry (yr)

Risk-free rate

Volatility σ

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.

▶ Run in Python

Data Inspector

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

C = S N (d_{1}) - K e^{- r T} N (d_{2}) = 100 \cdot 0.580 - 100 e^{- 0.020} \cdot 0.510 = $8.01

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.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Students Educators Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Black-Scholes

Black-Scholes for a stock option Black-Scholes for a retirement fund Black-Scholes for a mortgage Black-Scholes for a bond ladder Black-Scholes for a crypto portfolio Black-Scholes for an index fund Black-Scholes for a savings plan Black-Scholes for a startup valuation

Frequently asked questions

Is this good for researchers?: Yes — this version of "Black-Scholes for a hedge position" is framed for researchers prototyping or validating an idea. Prototype fast, reproduce exactly, and share a citable, interactive version of your model.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.