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BTC/USD LIVE CHART
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MONTE CARLO 10Y PROJECTION
Forward Price Probability Distribution
dS = μS·dt + σS·dW | GBM with GARCH(1,1) | σ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁
VOLATILITY SURFACE
Rolling Window × Lookback
σ(w,t) = √(252/w · Σ(rₜ₋ᵢ − r̄)²) | Annualized Realized Vol
PRICE PROBABILITY DENSITY
Time × Price × Probability
f(S,t) = (1/Sσ√(2πt)) · exp(-(ln(S/S₀)-(μ-σ²/2)t)²/(2σ²t))
LOG RETURNS DISTRIBUTION
Empirical vs Normal vs Student-t
r = ln(Sₜ/Sₜ₋₁) | Skew = E[(r-μ)³]/σ³ | Kurt = E[(r-μ)⁴]/σ⁴
DRAWDOWN ANALYSIS
Max Drawdown & Underwater Equity
DD(t) = (Peak(t) - S(t)) / Peak(t) | MDD = max(DD(t))
ROLLING RISK METRICS
Sharpe / Sortino / Calmar (90d)
Sharpe = (μ-Rf)/σ | Sortino = (μ-Rf)/σ_down | Calmar = CAGR/MDD
HURST EXPONENT & REGIME
Fractal Analysis
E[R(n)/S(n)] = C·nᴴ | H>0.5: Trend | H<0.5: Mean-Revert
MONTHLY RETURNS HEATMAP
Seasonality 2015–2026
AUTOCORRELATION
Serial Correlation & Memory
ACF(k) = Cov(rₜ,rₜ₋ₖ)/Var(rₜ) | 95% CI = ±1.96/√n
MONTE CARLO PRICE TARGETS
10Y Forward at Key Percentiles
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