Answer-first summary for fast verification
Answer: The estimate decreased due to the effect of the long-run average variance rate.
## 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.
Author: LeetQuiz .
Ultimate access to all questions.
A risk analyst is interpreting the results derived from applying a GARCH (1,1) model for estimating the current trading day's price volatility of a stock. Selected inputs to the model are provided below:
Assuming α, β, and γ are held constant, how did the price volatility estimate calculated using GARCH (1,1) change from the previous day's value to the current day's value?
A
The estimate increased due to the effect of the previous trading day's return.
B
The estimate decreased due to the effect of the previous trading day's return.
C
The estimate increased due to the effect of the long-run average variance rate.
D
The estimate decreased due to the effect of the long-run average variance rate.
No comments yet.