Monte Carlo Simulator

Historical Cycle Statistics

Per-cycle distribution parameters derived from daily log returns. Note how volatility and mean returns decline with each successive cycle.

Cycle	Mean Daily	Daily Vol	Skew	Excess Kurt	t-DoF	Ann. Vol

Cycle Regime Comparison

Compare what happens if you retire into different cycle volatility environments.

Compare Cycles

Simulation Parameters

Volatility Regime

Mean Reversion Speed

Controls how strongly price reverts to the power law trend. Higher κ = faster reversion, tighter corridor.

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Withdrawal Strategy (optional)

USD withdrawals convert to BTC at the simulated price each day. Multiple withdrawal types can be combined.

Backtest: Model vs Reality

Run a simulation using each halving cycle's own volatility regime, then overlay the actual BTC price path. How well does the OU model capture reality?

Methodology

Power Law Model: Santostasi/Perrenod model with β = 5.688, log₁₀(A) = −16.493. Time variable is days since genesis (Jan 3, 2009).

Ornstein-Uhlenbeck Process: The log₁₀-residual (distance from power law trend in log space) follows a mean-reverting OU process: dr = −κ(r − μ)dt + σ_OU√dt · Z, where Z ~ Student's t for fat tails. This ensures paths oscillate around the power law corridor rather than diverging to infinity. The mean-reversion speed κ controls corridor tightness; σ_OU is calibrated so stationary variance matches observed cycle residual variance.

Downside Floor (−2σ): Simulated residuals are clamped at −2σ (where σ = 0.2 is the model's long-run log₁₀-residual scale). In 15+ years of trading history, Bitcoin has never breached the −2σ power law floor — even during the deepest drawdowns (2011, 2015, 2018, 2022) the price has consistently bounced above this level. The floor acts as a structural lower bound in the simulation, preventing paths from exploring deep discounts that have no historical precedent. Caveat: past adherence to this floor does not guarantee it will hold in the future. A black-swan event, regulatory shock, or structural break in the power law could push prices below −2σ. This constraint makes the simulation optimistic on the downside.

Cycle Regimes: Per-cycle residual parameters (mean, standard deviation, tail thickness) are fitted from historical data. For blended modes, the cycle regime is re-drawn annually. Cycle 5 is excluded from default blends as it is still incomplete.

Withdrawal: Three modes: fixed USD (converted to BTC at simulated price), fixed BTC, or percentage-based. Multiple types can be combined. Ruin occurs when the BTC stack reaches zero.

Computation runs entirely client-side using Web Workers. No data is sent to any server.