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

A risk analyst at a bank estimates the distribution of daily P&L using 500 historical observations. She replaces the histogram with a kernel density estimate. Which statement best describes the main benefit of this change for estimating Value-at-Risk?

Kernel density estimation smooths the discrete historical sample into a continuous density, so VaR quantiles can be read from a smooth curve instead of jumping between observations. It remains non-parametric and still depends on past data, and it imposes neither normality nor an extreme value tail form.

  1. AIt removes the need to assume that past returns are informative about future returns
  2. BIt smooths the empirical distribution so that quantiles can be read from a continuous density rather than from discrete jumpsCorrect
  3. CIt guarantees that the estimated tail follows a generalized Pareto distribution
  4. DIt converts the historical sample into a normal distribution with the same mean and variance

Explanation

A kernel estimator spreads each observation over a neighborhood, producing a continuous density from which quantiles can be obtained more smoothly. It still relies on historical data, so the first option is wrong. It does not impose normality or a GPD tail.

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