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

A bank's market risk team has 1,000 daily P&L observations and wants a VaR estimate that reflects recent market conditions more heavily while also producing a smooth quantile. Which approach combines these goals most directly?

Combining age-weighted observations with kernel smoothing meets both goals: weights emphasise recent data, and the kernel produces a continuous density from which the VaR quantile is read. The other choices are parametric, ignore the confidence level, or misapply tail models.

  1. AApply age-weighted observations and then use a kernel-smoothed density of the weighted data to read off the quantileCorrect
  2. BFit a normal distribution to the most recent 10 observations only
  3. CUse the single worst observation in the sample as the VaR
  4. DApply a generalized Pareto fit to the entire sample, including gains

Explanation

Age weighting gives recent observations more influence, and kernel smoothing of the weighted data yields a continuous density from which a quantile is read. Using 10 observations is statistically unreliable and parametric, the worst observation ignores the confidence level, and a Pareto fit applies only to tail exceedances.

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