Do I need to install anything?

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

For K-12 Students · Monte Carlo (GBM)

Monte Carlo (GBM) for a margin trade

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 margin trade live below — adjust the inputs and watch it respond, right in your browser.

Monte Carlo Price SimulationLive

geometric Brownian motion

Controls

Presets

Initial price S₀

Expected return μ

Volatility σ

Horizon (years)

Geometric Brownian motion models a price with constant drift and random volatility — the assumption behind Black-Scholes. Running hundreds of simulated paths reveals the full distribution of outcomes, not just an average. Educational tool, not investment advice.

▶ Run in Python

Data Inspector

Median outcome$0

5th percentile$0

95th percentile$0

Governing equation

S_{t + Δ t} = S_{t} e^{(0.07 - \frac{0. 2 ^{2}}{2}) Δ t + 0.2 Δ t Z}, \tilde{S}_{1} \approx $0

Reading this result: Median outcome is about $0, just under the drift-only $107 — GBM compounds in log-space, so volatility always pulls the typical path below the average.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Monte Carlo (GBM) for a margin trade" 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.