Modeling Market Turbulence: GARCH, EGARCH & HAR for Volatility Forecasting

1. Why Dedicated Volatility Models

Volatility has distinct properties:

Heavy tails: extreme moves cluster together
Clustering: high vol periods follow high vol periods
Mean reversion: volatility tends to revert to long-term average

Risk management, position sizing, and VaR all depend on accurate vol forecasts.

Volatility Clustering Visual

Show Squared Returns

Highlight High-Vol Clusters

2. GARCH Family

Intuition: today's volatility depends on yesterday's shock and yesterday's volatility.

GARCH(1,1):

r_t = σ_t ε_t, ε_t ~ N(0,1)

σ_t² = ω + α r_{t-1}² + β σ_{t-1}²

where ω > 0, α ≥ 0, β ≥ 0, and α + β < 1 for stationarity

EGARCH / GJR-GARCH: allow for asymmetry (downside shocks impact vol more).

EGARCH(1,1):

log(σ_t²) = ω + α(|ε_{t-1}| - E|ε_{t-1}|) + γε_{t-1} + β log(σ_{t-1}²)

The γ term captures asymmetry: negative shocks (γ < 0) increase volatility more than positive shocks

GARCH Response to Shock

Size of Shock at Time t: 2.0%

Note how the large shock raises volatility and then gradually mean reverts. This demonstrates the clustering property of volatility: high vol periods follow high vol periods.

3. HAR-RV

Heterogeneous AutoRegressive model for realized volatility. Uses lags at multiple horizons: 1-day, 5-day, 22-day, etc.

Intuition: traders with different time horizons contribute to volatility dynamics.

4. Use in volarixs

Vol targets for equities, FX, indices. Input into:

Risk-adjusted signals
Regime classification
Position sizing rules in alpha factory

GARCH

EGARCH

HAR-RV

1. Why Dedicated Volatility Models

Volatility has distinct properties:

Heavy tails: extreme moves cluster together

Clustering: high vol periods follow high vol periods

Mean reversion: volatility tends to revert to long-term average