INV4801
Assignment 2
DUE : 19 AUGUST 2026
, INV4801 – Assignment 02: Worked Solutions
Unique Number: 236775 | Due: Wednesday, 19 August 2026, 20:00
Question 1(a): GARCH(1,1) — Re-parameterised Model
Given: α = -0.08, γ = 0.00010, β = 0.35; previous period estimated variance σ²ₜ₋₁ = 0.0144; current period
return is 7.77% above the expected value (i.e. the shock uₜ₋₁ = 0.0777). (The 1% daily standard deviation
and the 1.2% comparable-company standard deviation are supplementary/contextual figures not
required for parts (i)–(iii).)
(i) Conditional variance for today
The re-parameterised GARCH(1,1) model is:
σ²ₜ = γ + α·u²ₜ₋₁ + β·σ²ₜ₋₁
where γ is the (already weighted) long-run variance component (ω), α is the weight on the squared
surprise/shock, and β is the weight on last period's variance.
Step 1 – square the shock: u²ₜ₋₁ = (0.0777)² = 0.00603729
Step 2 – substitute into the model:
σ²ₜ = 0.00010 + (−0.08 × 0.00603729) + (0.35 × 0.0144)
σ²ₜ = 0.00010 − 0.00048298 + 0.00504000
σ²ₜ = 0.00465702
Answer: Conditional variance for today, σ²ₜ ≈ 0.004657 (0.4657%).
(ii) Conditional standard deviation for today
σₜ = √σ²ₜ = √0.00465702
Answer: σₜ ≈ 0.06824, i.e. approximately 6.82% per day.
Assignment 2
DUE : 19 AUGUST 2026
, INV4801 – Assignment 02: Worked Solutions
Unique Number: 236775 | Due: Wednesday, 19 August 2026, 20:00
Question 1(a): GARCH(1,1) — Re-parameterised Model
Given: α = -0.08, γ = 0.00010, β = 0.35; previous period estimated variance σ²ₜ₋₁ = 0.0144; current period
return is 7.77% above the expected value (i.e. the shock uₜ₋₁ = 0.0777). (The 1% daily standard deviation
and the 1.2% comparable-company standard deviation are supplementary/contextual figures not
required for parts (i)–(iii).)
(i) Conditional variance for today
The re-parameterised GARCH(1,1) model is:
σ²ₜ = γ + α·u²ₜ₋₁ + β·σ²ₜ₋₁
where γ is the (already weighted) long-run variance component (ω), α is the weight on the squared
surprise/shock, and β is the weight on last period's variance.
Step 1 – square the shock: u²ₜ₋₁ = (0.0777)² = 0.00603729
Step 2 – substitute into the model:
σ²ₜ = 0.00010 + (−0.08 × 0.00603729) + (0.35 × 0.0144)
σ²ₜ = 0.00010 − 0.00048298 + 0.00504000
σ²ₜ = 0.00465702
Answer: Conditional variance for today, σ²ₜ ≈ 0.004657 (0.4657%).
(ii) Conditional standard deviation for today
σₜ = √σ²ₜ = √0.00465702
Answer: σₜ ≈ 0.06824, i.e. approximately 6.82% per day.
