Skip to content

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

A risk analyst at a bank estimates the 99% VaR of a trading book using 500 daily P&L observations. She replaces the plain historical simulation histogram with a smoothed non-parametric density estimate built with a kernel. Which statement best describes the main purpose of the kernel in this approach?

A kernel smooths the data by placing a local weighted bump around each observation, giving a continuous density estimate without gaps or steps. It does not impose a normal shape, fit tail distributions, or weight observations by age, which are other methods.

  1. AIt places a smooth local weighting around each observation so the estimated density has no gaps or jagged steps between data pointsCorrect
  2. BIt assumes returns follow a normal distribution and rescales the data by the sample standard deviation
  3. CIt fits a generalized Pareto distribution to losses beyond a chosen threshold
  4. DIt assigns exponentially declining weights to older observations based on a decay factor

Explanation

Kernel density estimation spreads each observation into a smooth local bump, producing a continuous density estimate from discrete data. The normal-fit option describes a parametric approach, the Pareto option is extreme value theory, and the decay-weight option is the age-weighted (BRW) historical simulation.

Did you get it right without looking?

One question tells you little. A timed set on Non-parametric Approaches shows your real accuracy, how long you take and where you lose marks.

Practise Non-parametric ApproachesFree diagnostic mock

More Non-parametric Approaches questions