Do I need to install anything?

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

For Students · Monte Carlo (GBM)

Monte Carlo (GBM) for a dollar-cost-average plan

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a dollar-cost-average plan 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.

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

or unlock everything with Pro →

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

More with Monte Carlo (GBM)

Monte Carlo (GBM) for a stock option Monte Carlo (GBM) for a retirement fund Monte Carlo (GBM) for a mortgage Monte Carlo (GBM) for a bond ladder Monte Carlo (GBM) for a crypto portfolio Monte Carlo (GBM) for an index fund Monte Carlo (GBM) for a savings plan Monte Carlo (GBM) for a startup valuation

Frequently asked questions

Is this good for students?: Yes — this version of "Monte Carlo (GBM) for a dollar-cost-average plan" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.