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.
## Explanation Let's analyze each option: **Option A**: Incorrect. The EWMA model is actually a special case of GARCH(1,1) where ω = 0 and α + β = 1, not where long-run volatility is zero. In GARCH(1,1), long-run variance is ω/(1-α-β), so setting this to zero would require ω = 0, but that's not the complete condition for EWMA. **Option B**: Incorrect. GARCH(1,1) variance is a weighted average of three components: long-run variance, prior day's estimated variance, and prior day's squared return. The formula is: σ²ₜ = ω + αr²ₜ₋₁ + βσ²ₜ₋₁. **Option C**: Incorrect. The relative weights depend on the specific parameter values chosen. There's no inherent relationship that GARCH(1,1) always assigns higher weight to prior variance than EWMA. **Option D**: **CORRECT**. The EWMA model variance is indeed a weighted average of the prior day's estimated variance and the prior day's squared return. The formula is: σ²ₜ = λσ²ₜ₋₁ + (1-λ)r²ₜ₋₁, where λ is the decay factor. **Key Insight**: EWMA is a simplified version of GARCH(1,1) that doesn't include a long-run variance component, making it purely a weighted average of past variance and squared returns.
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A junior risk analyst is modeling the volatility of a certain market variable. The analyst considers using either the EWMA or the GARCH (1,1) model. Which of the following statements 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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