EGARCH(1,1) Deep Dive

Exponential GARCH models log-variance — guaranteeing positivity — with an asymmetric γ term that makes negative shocks raise volatility more than positive ones.

Leverage γ

-0.08 (Present ✓)

Uncond. Vol (ann.)

3091.9%

NIC at z=+4

–

NIC at z=−4

–

Returns with ±2σₜ Envelope

Conditional Vol — log scale

Asymmetric News Impact Curve — γ creates skew

μ (mean)0.020

ω (log-const)0.04

α (size effect)0.12

γ (leverage, <0 = asymm)-0.08

β (persistence)0.97

Observations1000

Seed2

ln σ_{t}^{2} = ω + β ln σ_{t - 1}^{2} + α (∣ z_{t - 1} ∣ - E ∣ z ∣) + γ z_{t - 1}, z_{t} = r_{t} / σ_{t}

E ∣ z ∣ = 2/ π \approx 0.798; γ < 0 \Rightarrow leverage (bad news raises vol more)

Try γ = 0 to get a symmetric NIC (like GARCH). Set γ = −0.15 and watch the left half of the NIC curve lift significantly above the right — the leverage effect.

← GARCH GJR-GARCH →