Answer-first summary for fast verification
Answer: A variance estimated from the EWMA model is a weighted average of the prior day's estimated variance and the prior day's squared return.
The EWMA estimate of variance is a weighted average of the prior day's variance and prior day's squared return. - **A is incorrect**: EWMA is a particular case of GARCH(1,1) with the weight assigned to the long-run average variance rate as zero and the sum of the weights of the other two parameters equal to 1. - **B is incorrect**: Because there is also weight assigned to the long-run average variance rate in GARCH(1,1). - **C is incorrect**: Such a comparison can only be done under specific parameter configurations. **Key Points**: - EWMA: σ²ₙ = λσ²ₙ₋₁ + (1-λ)u²ₙ₋₁ - GARCH(1,1): σ²ₙ = ω + αu²ₙ₋₁ + βσ²ₙ₋₁ - EWMA is a special case of GARCH(1,1) where ω = 0 and α + β = 1
Author: LeetQuiz Editorial Team
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A junior risk analyst is modeling the volatility of a certain market variable and is trying to decide between EWMA and GARCH(1,1) models. Which of the following statements about the two models is correct?
A
The EWMA model is a special case of the GARCH(1,1) model with the additional assumption that the long-run volatility is zero.
B
A variance estimated from the GARCH(1,1) model is a weighted average of the prior day's estimated variance and the prior day's squared return.
C
The GARCH(1,1) model assigns a higher weight to the prior day's estimated variance than the EWMA model.
D
A variance estimated from the EWMA model is a weighted average of the prior day's estimated variance and the prior day's squared return.
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