Methodology

How our models work, what data we use, and the limits of mathematical projections.

Monte Carlo Simulation

How It Works

We run thousands of possible Bitcoin price paths using Geometric Brownian Motion (GBM). Each simulation assumes Bitcoin prices follow a random walk with:

  • Drift: Average annual growth rate (default: 15%)
  • Volatility: Year-over-year price variation (default: 80%)
  • Log-normal distribution: Prices can't go negative

What We Report

From 10,000 simulations, we show you percentiles:

  • 10th percentile: Pessimistic outcome (1 in 10 chance of worse)
  • 50th percentile (median): Middle outcome
  • 90th percentile: Optimistic outcome (1 in 10 chance of better)

Critical Limitations

  • Fat tails: Monte Carlo underestimates extreme events (crashes, manias)
  • Regime changes: Can't predict regulatory shifts, adoption phases, or market structure evolution
  • Correlation assumptions: Real markets have complex dependencies we can't capture
  • Stationary assumptions: Historical patterns may not continue

Power-Law Floor Model

Conservative Baseline

Alongside Monte Carlo, we show a "power-law floor" scenario based on Bitcoin's historical price growth pattern. This provides a more conservative baseline.

The power-law model suggests Bitcoin price follows a predictable log-linear trend over multi-year periods, with cyclical deviations around this trend.

Key References

  • Bitbo Charts: Power-law corridor and support/resistance analysis
  • bitcoinfairprice.com: Power-law regression models
  • Academic research: Santostasi and others on Bitcoin's power-law behavior

Model Limitations

  • Past performance: Historical trends may not continue indefinitely
  • Diminishing returns: Power-law may break down as Bitcoin matures
  • Market size constraints: Physical limits to how large Bitcoin can become

Data Sources

Bitcoin Price Data

  • Source: CoinGecko API
  • Update frequency: Every 6 hours via automated pipeline
  • Fallback: Static snapshot if API unavailable
  • Historical data: Daily prices from 2010-present

Gold Market Data

  • Price source: PAX Gold (PAXG) token via CoinGecko
  • Supply estimate: ~200,000 tonnes above-ground gold
  • Market cap calculation: Price × estimated supply
  • Why PAXG: Tokenized physical gold, transparent pricing

Global Wealth Data

  • Source: UBS Global Wealth Report 2025
  • Total estimate: ~$471 trillion
  • Includes: Real estate, financial assets, commodities
  • Geographic coverage: Global household wealth

Halving Schedule

  • Block height tracking: Real-time blockchain data
  • Timing estimates: Based on 10-minute average block times
  • Next halving: ~Block 1,050,000 (April 2028 ±2 weeks)
  • Historical dates: Verified blockchain events

Key Assumptions & Limitations

Retirement Planning Assumptions

  • 4% withdrawal rule: Standard assumption for sustainable retirement income
  • Constant real purchasing power: Income needs remain constant in today's dollars
  • No other assets: We only model Bitcoin holdings, not diversified portfolios
  • Tax simplification: Optional flat tax rate (default 22%)

What We Don't Model

  • Regulatory risk: Government bans, restrictions, or confiscation
  • Technical risk: Bitcoin protocol failures or security breaches
  • Liquidity constraints: Assumes you can always sell Bitcoin at market price
  • Sequence of returns risk: Order of gains/losses during retirement
  • Health/longevity changes: Unexpected medical costs or lifespan changes

Important Disclaimers

  • Not financial advice: These are mathematical projections, not investment recommendations
  • High volatility asset: Bitcoin can lose 50-80% of value in bear markets
  • Experimental technology: Bitcoin is only 15 years old with limited historical data
  • Total loss possible: Bitcoin could theoretically go to zero

Model Validation & Backtesting

How We Test Our Models

  • Historical backtesting: Run models on past data to check accuracy
  • Out-of-sample testing: Test on time periods not used for model fitting
  • Stress testing: See how models perform during extreme market conditions
  • Parameter sensitivity: Check how small changes affect outcomes

Continuous Improvement

We regularly update our models based on new data and research. Model parameters and assumptions are adjusted as Bitcoin markets mature and new information becomes available.

Last model update: December 2024 (post-ETF approval data integration)

Questions about our methodology? Get in touch