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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 correct answer is 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. The explanation for this is that the EWMA model uses a constant weight for the squared return of the previous day and a complementary weight for the previous day's variance estimate. This approach allows for a more gradual adjustment of the variance estimate in response to new information, compared to the GARCH(1,1) model. Option A is incorrect because the EWMA model is not a special case of the GARCH(1,1) model with the long-run volatility set to zero. Instead, the EWMA model is a simplified version of the GARCH model where the long-term variance is not explicitly modeled. Option B is incorrect because the GARCH(1,1) model includes a weighted average of not only the prior day's squared return but also the long-run average variance rate, which is not mentioned in this option. Option C is incorrect because the comparison of weights between the GARCH(1,1) and EWMA models can only be made under specific parameter configurations, and it is not universally true that GARCH(1,1) assigns a higher weight to the prior day's estimated variance than the EWMA model does.
Author: LeetQuiz Editorial Team
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A newly appointed entry-level risk analyst is in the process of constructing a model to quantify the volatility of a specific market variable. The analyst is deliberating between two volatility models: the Exponentially Weighted Moving Average (EWMA) and the Generalized Autoregressive Conditional Heteroskedasticity (GARCH(1,1)). Which of the following statements correctly characterizes the attributes of these two models?
A
1 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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