Do I need to install anything?

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

For K-12 Students · Delta Hedging Sim

Delta Hedging Sim for a Black-Scholes option

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a Black-Scholes option live below — adjust the inputs and watch it respond, right in your browser.

Black Scholes

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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.

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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.

↓

Option Payoff

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Option Strategy PayoffLive

profit/loss at expiry

Controls

Presets

Center strike

An option strategy's payoff diagram plots profit or loss against the underlying price at expiration. Combining calls and puts at different strikes shapes the curve — capping risk, capturing volatility, or generating income. Educational tool, not investment advice.

▶ Run in Python

Data Inspector

Max profit$5.00

Max loss$-5.00

Net debit/credit$5.00

Legs2

Governing equation

Π (S) = i \sum q_{i} [max (S - K_{i}, 0)_{call}, max (K_{i} - S, 0)_{put} - p_{i}], K = 100

Reading this result: Both profit and loss are capped, so this is a defined-risk position — you trade unlimited upside for a known worst case.

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

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Delta Hedging Sim for a Black-Scholes option" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.