Scenario Simulator

// the model

The simulator runs 10,000 hypothetical price paths under Geometric Brownian Motion (GBM) — the same stochastic process that backs Black-Scholes options pricing. Each path takes daily steps; at each step the price drifts by your annual-drift assumption and gets randomly shocked by your volatility.

S_{t+1} = S_t · exp((μ − σ²/2)·dt + σ·√dt·Z)
  Z ~ N(0,1)
  μ  = annual drift
  σ  = annual volatility
  dt = 1/365

After all 10k paths complete, prices are sorted by day and the 10th / 50th / 90th percentiles are extracted to draw the cone. The terminal-day distribution becomes the histogram.

// the four assumptions

// reading the chart

Solid green (P50) — median outcome. Half of paths end above, half below. Not the same as the average; for log-normal distributions the mean sits above the median.
Cyan dashed (P90) — bull case. 10% of paths end above this.
Red dashed (P10) — bear case. 10% of paths end below this.
The fill between P10 and P90 is your 80% confidence band.
Histogram: same terminal-day data as a distribution. Right-skewed because GBM is log-normal — price can't go negative, but can blow up to the upside.

// volatility drag

The most non-obvious property of GBM: P50 sits below spot at high vol, even when drift is positive.

Why: the median grows at μ − σ²/2 per year — annual drift minus half the variance. With σ = 0.40 (40% vol), that's a built-in −8% per year headwind on the median. To get P50 at par with spot you need drift = σ²/2 = 8%; to get P50 above spot, even more.

This is the math reason a low-vol asset compounding at 8% a year outperforms a high-vol asset compounding at 8% a year. It's why leverage that survives upside whipsaws still bleeds capital. And it's why “expected return” alone is a misleading measure for size and stop decisions.

// how to use it

Is my exit target realistic?

Set spot to current price, vol to the asset's realized 30/90-day vol, drift to your thesis, horizon to your intended trade window. If your target sits above the P90 line, you're betting on a top-decile outcome — not impossible, but be honest about the odds.

Where should my stop go?

P10 at your horizon is roughly the 1-in-10 bear case for normal market noise. If your stop sits above the P10 line, you'll get stopped out by noise more often than by an actual thesis break. Drop the stop below P10 — or accept higher false-stop frequency as a cost.

Should I lever up this trade?

If the P10 terminal price puts you below your liquidation price for the size you're considering, no. Run the simulation at your worst-case-vol assumption, not the current value — vol can spike without warning.

Is buying the top half of this range a coin flip?

No — because of skew. The median is below the arithmetic mean of terminal prices. Buying at P50 means more than half your future paths end below P50. That sounds tautological but it's worth saying out loud.

// caveats

GBM is a useful approximation, not reality. Things it does NOT model:

Fat tails. Real crypto has way more 5σ days than a normal distribution predicts. P10 is too optimistic about downside.
Jump risk. No LUNA-style instant collapse, no exchange insolvency, no rug pull. Don't trust the cone for tail-event sizing.
Path dependency. “If price hits X first then Y” requires path-aware simulation; this is endpoint-only.
Correlation. Single asset only. A bear case in BTC is usually a worse bear case in your alts.
Regime changes. Volatility clusters; recent vol is a better predictor of next-week vol than long-run vol. The model uses one constant σ.

Use as a sanity-check on size, target, and stop math — not as a forecast.