S(t + Δt) = S(t) × exp[(μ − σ²/2)Δt + σ√Δt · Z], with Z drawn from a standard normal distribution. 50–50,000 independent paths, 120 time steps, and a fixed seed make the same inputs reproducible. All requested paths contribute to statistics; the chart shows up to 80 paths sampled across the simulation. A starting value of 100 gives an index view; enter a price manually for a price-scale view.

Inputs are illustrative assumptions, not estimates fitted to the prices below. The instrument selection does not supply historical returns, live quotes, or fitted volatility. Crypto selections suggest a 365-day basis; other instruments suggest 252 trading days. Both remain editable. Constant drift and volatility, independent shocks, and no jumps, fees, leverage or liquidity effects. The band is the pointwise 5th–95th percentile range under these assumptions; it is not a guarantee or a trading signal.