Explanation:
The correct answer is C.
Filtered historical simulation adjusts historical returns by accounting for changing volatility (typically modeled using GARCH or similar methods). This reduces the noise in historical data, particularly during periods of market stress, leading to more stable and narrower confidence intervals compared to standard historical simulation, which relies purely on raw historical data.
A is incorrect: Confidence intervals for VaR estimates are often asymmetric, especially in methods that rely on tail risk modeling (e.g., FHS or GARCH). Tail distributions are typically skewed, leading to uneven confidence bounds.
B is incorrect: Using more data generally reduces sampling variability, leading to narrower confidence intervals, not wider ones. Larger datasets improve the reliability of the VaR estimate by reducing uncertainty.
D is incorrect: There's no "convincing evidence that one method or the other produces tighter confidence intervals on a consistent basis" when comparing order statistics and bootstrapping with historical simulation VaR.
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Q.6468 A risk analyst is comparing different methods for constructing confidence intervals for one-day 99% VaR estimates of the S&P 500. They are considering historical simulation, GARCH, and filtered historical simulation (FHS) VaR, along with various confidence interval estimation techniques, including order statistics and bootstrapping. Based on empirical studies, which of the following statements regarding the width of confidence intervals is correct?
A
Confidence intervals for VaR estimates are typically symmetric around the point estimate.
B
Using more data to estimate VaR generally leads to wider confidence intervals.
C
Filtered historical simulation (FHS) tends to produce narrower confidence intervals compared to historical simulation, particularly during stress periods.
D
Order statistics consistently produces tighter confidence intervals than bootstrapping when used with historical simulation VaR.
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