Explanation

The GARCH (1,1) model formula is: σₙ² = γVₗ + αrₙ₋₁² + βσₙ₋₁²

Given data:

• Previous trading day's return (rₙ₋₁): -3% = -0.03
• Previous variance rate (σₙ₋₁²): 0.0009
• Long-run average variance rate (Vₗ): 0.0001

Step 1: Calculate previous volatility Previous volatility (σₙ₋₁) = √(σₙ₋₁²) = √(0.0009) = 0.03 (or 3%)

Step 2: Analyze the components

• The squared return rₙ₋₁² = (-0.03)² = 0.0009, which equals the previous variance rate (σₙ₋₁² = 0.0009)
• The long-run average variance rate Vₗ = 0.0001 corresponds to volatility of √(0.0001) = 0.01 (or 1%)

Step 3: Determine the change Since rₙ₋₁² = σₙ₋₁², the squared return term (αrₙ₋₁²) does not change the volatility estimate from the previous level. However, the long-run average variance rate (Vₗ = 0.0001) corresponds to a lower volatility (1%) than the previous volatility (3%), so this component pulls the current volatility estimate downward.

Therefore, the volatility estimate decreased due to the effect of the long-run average variance rate.

Why other options are incorrect:

• A & B: The previous trading day's return, when squared, equals the previous variance rate, so it doesn't change the volatility estimate.
• C: The long-run average variance rate actually decreases the volatility estimate, not increases it.