Answer-first summary for fast verification
Answer: $\alpha = 0.075637$ and $\beta = 0.923363$
## Explanation For a GARCH(1,1) process to be stable, the parameters must satisfy the following conditions: 1. All parameters (α, β, γ) must be positive 2. The sum of α + β + γ must equal 1 3. The sum of α + β must be less than 1 (since γ = 1 - α - β > 0) Let's verify each option: **Option A:** α = 0.073637, β = 0.927363 Sum = 0.073637 + 0.927363 = 1.001000 > 1 ❌ Not stable (sum > 1) **Option B:** α = 0.075637, β = 0.923363 Sum = 0.075637 + 0.923363 = 0.999000 < 1 γ = 1 - 0.999000 = 0.001000 > 0 ✅ Stable (sum < 1, γ > 0) **Option C:** α = 0.084637, β = 0.916363 Sum = 0.084637 + 0.916363 = 1.001000 > 1 ❌ Not stable (sum > 1) **Option D:** α = 0.086637, β = 0.914363 Sum = 0.086637 + 0.914363 = 1.001000 > 1 ❌ Not stable (sum > 1) Only Option B satisfies the stability condition where α + β < 1, ensuring that γ = 1 - α - β > 0, and all parameters are positive.
Author: LeetQuiz .
Ultimate access to all questions.
A risk analyst is estimating the variance of returns on a stock index for the next trading day. The analyst uses the following GARCH (1,1) model:
where , , and represent the index variance on day , return on day , and volatility on day , respectively. If the expected value of the return is constant over time, which combination of values for and would result in a stable GARCH (1,1) process?
A
and
B
and
C
and
D
and
No comments yet.