Each ribbon is one simulated path of an asset price under geometric Brownian motion: at every timestep, price moves by a deterministic drift plus random volatility-scaled noise. Fanning hundreds of these paths out from a common starting price approximates the full distribution of possible future outcomes — the basis of Monte Carlo financial models.
dS = μS dt + σS dW
S(t+dt) = S(t) * exp((μ - σ²/2)dt + σ√dt·Z), Z~N(0,1)
VaR(5%) = start - 5th percentile of S(T)
- Volatility σ — widens the spread of the path fan; higher σ means more risk.
- Drift μ — tilts the whole fan up or down (expected annual return).
- Number of paths — more Monte Carlo samples for a smoother risk estimate.
- Time horizon — how many years each path is simulated forward.
- Resimulate — draws a fresh batch of random paths with the current settings.
Investment banks and portfolio managers run thousands of GBM Monte Carlo paths like these to estimate value-at-risk and stress-test portfolios before allocating capital.