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FRM Part I · FRM Exam Part I · Operational Risk

In the loss distribution approach (LDA) to operational risk capital, a bank models the number of loss events per year and the size of each loss separately. Which pairing of distributions is the most common choice for frequency and severity respectively?

The most common LDA pairing is Poisson for loss frequency and lognormal for loss severity. Frequency counts are non-negative integers, which suits Poisson, while losses are positive and heavily right-skewed, which suits lognormal. Normal or uniform severity would understate the tail.

  1. ANormal for frequency; uniform for severity
  2. BPoisson for frequency; lognormal for severityCorrect
  3. CLognormal for frequency; Poisson for severity
  4. DBinomial for frequency; normal for severity

Explanation

LDA typically uses a discrete count distribution such as Poisson for frequency and a skewed, heavy-tailed distribution such as lognormal for severity. Frequency must be a non-negative integer, ruling out normal and lognormal. Severity is positive and right-skewed, so normal or uniform is a poor fit.

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