Monte Carlo · Geometric Brownian Motion

10,000 Possible Futures

The same math banks use to price options and size risk. Each faint line is one simulated future for a stock; together they map the cone of uncertainty. Drag the dials, then read the odds a quant actually cares about — probability of profit, 95% Value-at-Risk, and the percentile fan.

Simulated price paths 252 trading days · 1 year horizon
Start price S₀$100
Drift μ (annual)8%
Volatility σ (annual)18%
Horizon252d
Paths400
Distribution of outcomes at horizon terminal price Sₜ
profit vs S₀ loss vs S₀ median (P50) start S₀
The oddsn = 400
Probability of profit
Expected Sₜ
Median (P50)
95% VaR (1y)
5% chance of losing ≥ this
90% range (P5–P95)
where 9 of 10 futures land