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FRM Part II · FRM Exam Part II · Non-parametric Approaches

An analyst compares a plain historical simulation estimate of VaR with a kernel-smoothed estimate from the same 250-day sample. The data contain only a few observations in the extreme left tail. Which is the most accurate comparison?

Kernel smoothing yields a VaR from a continuous density, avoiding reliance on one order statistic, but it is still based on observed data and cannot reliably extrapolate beyond the worst observed losses. Extreme value methods are better suited to extreme tail estimation.

  1. AThe kernel approach can produce a VaR between observed data points, avoiding the dependence on a single order statistic, but it still cannot reliably extrapolate beyond the worst observed lossesCorrect
  2. BThe kernel approach removes the need for a large sample and accurately predicts losses far beyond the worst observation
  3. CThe kernel approach gives a VaR that is always identical to the historical simulation percentile
  4. DThe kernel approach requires the assumption of constant volatility, which historical simulation does not

Explanation

Smoothing lets the quantile be read from a continuous density, so VaR does not jump between order statistics. However, kernels are built from the observed data and give little information on losses beyond the sample extremes; extreme value theory is better suited to that. The other options misstate this.

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