The green bar chart is a stock price following geometric Brownian motion — the same random-walk model used to derive the Black – Scholes option pricing formula. Each trading day the price is nudged by a deterministic drift plus a random shock scaled by volatility, so returns compound rather than add: a stock can't go below zero, and big moves get proportionally bigger as the price rises.
S(t+dt) = S(t) · exp[(μ − σ²/2)dt + σ√dt · Z]
Z ~ standard normal (Box–Muller)
The blue ribbon is a government bond price, modeled with a mean-reverting short-rate process (Vasicek-style): its underlying yield is pulled back toward a long-run level, so unlike the stock it doesn't drift away indefinitely — it wanders and then relaxes, which is why bond prices are calmer and yields and prices move inversely.
r(t+dt) = r(t) + κ(θ − r(t))dt + η√dt · Z
Bond price ≈ par / (1 + r)^duration
- Drift μ — the stock's expected annual return; higher drift trends the price upward over time, lower or negative drift trends it down.
- Volatility σ — how large the random daily shocks are; higher volatility makes the bars swing wider and the max drawdown deepen.
- Simulation speed — how many trading days advance per second, so you can watch a full year compress into seconds or slow it down to see individual daily moves.
- Max drawdown — the largest peak-to-trough decline the stock has experienced so far, the standard risk metric portfolio managers watch.
Real-world relevance: this is exactly the pairing behind classic portfolio theory — a volatile, growth-seeking stock diversified against a calmer, mean-reverting bond — and the same GBM engine underlies option pricing, Monte Carlo risk models (VaR), and robo-advisor rebalancing algorithms.