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    Finance / GARCH Volatility Forecasting Solver

    GARCH Volatility Calculator

    Forecast volatility with a GARCH model. Runs locally in your browser — no signup, no data leaves your device. Editorial guide in progress.

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    ZorvLabs · Volatility forecasting

    GARCH Volatility Forecast Calculator

    Univariate GARCH(1,1) conditional variance recursion with exact multi-step forecasts, log-likelihood diagnostics, fan bands, and 2D, 3D, and combined views.
    Stability
    stationary
    Persistence φ = α + β = 0.98000
    One-step variance
    0.00024114
    σ²_{t+1} exact recursion
    Long-run variance
    0.00100000
    ω / (1 − α − β)
    Horizon variance
    0.00057761
    σ² at h = 30
    Half-life
    34.3096
    ln(0.5)/ln(φ)
    View mode
    3D surface
    Display scale
    Mean return μ
    GARCH constant ω
    ARCH coefficient α
    GARCH coefficient β
    Initial variance σ²_0
    Forecast horizon h
    Scenario length
    Fan quantile z-score
    Density window (σ)
    Surface α min
    Surface α max
    Surface β min
    Surface β max
    Surface X resolution
    Surface Y resolution
    Persistence φ
    0.980000
    α + β
    Stationarity
    Yes
    φ < 1 required
    Scenario logL
    557.3242
    Gaussian filter diagnostic
    One-step σ
    0.015529
    √σ²_{t+1}
    ARCH/GARCH recursion: σ²_t = ω + αε²_{t-1} + βσ²_{t-1}.
    Forecast: E_t[σ²_{t+h}] = σ̄² + (α+β)^{h-1}(σ²_{t+1} − σ̄²).
    2D filtered path
    Deterministic scenario shocks, conditional variance, and realized squared innovations
    Scenario recursion · σ²tvariance0.035.871.6107.4143.2179.04.289e-90.00010.00030.00040.00050.0007conditional σ²_trealized ε²_t
    2D forecast term structure
    Exact multi-step conditional variance forecast
    Forecast variance term structurehσ²1.06.812.618.424.230.00.00020.00040.00050.00070.00080.0010forecast σ²_{t+h}unconditional σ²̄
    2D return fan chart
    Gaussian conditional return intervals from the forecast variance path
    Conditional return bandshreturn1.006.8012.6018.4024.2030.00-0.04-0.02-0.010.010.020.04Forecast meanFan band
    2D density slice
    Exact conditional density of returns at the selected horizon
    f(r_{t+h} | F_t), h = 30returnpdf-0.1-0.1-0.00.00.10.10.013.326.649.9613.2816.60return density
    3D exact surface
    Forecast variance over ARCH/GARCH coefficients at fixed horizon
    3D forecast-variance surface σ²_{t+h}(α,β)αβσ²surface grid58 × 64 cells · max σ² = 0.105990
    Key formulas
    Canonical ARCH / GARCH recursion and forecast algebra
    Engle (1982), ARCH(q): ε_t = σ_t z_t, σ_t² = ω + Σ α_i ε²_{t-i} with E[z_t]=0 and Var[z_t]=1.
    Bollerslev (1986), GARCH(p,q): σ_t² = ω + Σ α_i ε²_{t-i} + Σ β_j σ²_{t-j}.
    GARCH(1,1) forecast (φ = α+β < 1): E_t[σ²_{t+h}] = σ̄² + φ^(h−1)(σ²_{t+1} − σ̄²), σ̄² = ω/(1−φ).
    Gaussian log-likelihood: ℓ = −½ Σ [ log(2π) + log(σ_t²) + ε_t²/σ_t² ].
    This tool follows the standard GARCH(1,1) specification and the exact multi-step variance forecast formula.