GJR-GARCH(1,1) Deep Dive

The γ indicator switches additional variance impact on for negative shocks — illustrating the bad-news / good-news asymmetry via the kinked News Impact Curve.

Stationary

Yes ✓

Uncond. Vol (ann.)

1587.5%

Bad/Good news ratio

3.50

Leverage γ

0.100

Returns with Conditional Volatility Envelope

Kinked News Impact Curve — bad news (ε<0) hits harder

μ (mean)0.020

ω (constant)0.010

α (symmetric ARCH)0.04

γ (bad-news extra)0.10

β (persistence)0.90

Observations1000

Seed5

σ_{t}^{2} = ω + (α + γ 1_{ε_{t - 1} < 0}) ε_{t - 1}^{2} + β σ_{t - 1}^{2}

σ_{\infty}^{2} = \frac{ω}{1 - α - \frac{1}{2} γ - β}; bad-news ARCH impact: α + γ

Set γ = 0 to recover standard GARCH (symmetric NIC). Increase γ to widen the kink — the NIC slope on the negative side grows by exactly γ per unit ε².

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