LO 43.4: Explain how frequency and severity distributions of operational losses are obtained, including commonly used distributions and suitability guidelines for probability distributions.
Modeling Frequency
When developing a model of expected operational risk losses, the first step is to determine the likely frequency of events on an annual basis. The most common distribution for
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Topic 43 Cross Reference to GARP Assigned Reading – Girling, Chapter 12
modeling frequency is the Poisson distribution. This distribution uses only one parameter, \, which represents the average number of events in a given year, as well as the distributions mean and variance. In an LDA model, \ can be obtained by observing the historical number of internal loss events per year and then calculating the average.
The Poisson distribution represents the probability of a certain number of events occurring in a single year. As shown in Figure 2, lower values of \ produce more skewed and leptokurtic annual loss distributions than higher values of \.
Figure 2: Comparing Poisson Distributions
Modeling Severity
The next step in modeling expected operational risk losses is to determine the likely size (i.e., severity) of an event. The most common and least complex approach is to use a lognormal distribution. However, low frequency losses may be a better fit to distributions such as Generalized Gamma, Transformed Beta, Generalized Pareto, or Weibull. Regulators are interested in the selected distributions goodness of fit.
Regardless of the distribution selected, the probability density function must exhibit fat tails. Events that are more than three standard deviations from the mean are more likely to occur than in a normal distribution; thus, the distribution will be skewed as seen in Figure 3.
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Figure 3: Example Severity Probability Distribution
Topic 43 Cross Reference to GARP Assigned Reading – Girling, Chapter 12
Monte Carlo Simulation
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