A recap would be in order here: calculating operational risk capital is a multi-step process.

First, we fit curves to estimate the parameters to our chosen distribution types for frequency (eg,

Poisson), and severity (eg, lognormal). Note that these curves are fitted at the UoM level - which is

the lowest level of granularity at which modeling is carried out. Since there are many UoMs, there

are are many frequency and severity distributions. However what we are interested in is the loss

distribution for the entire bank from which the 99.9th percentile loss can be calculated. From the

multiple frequency and severity distributions we have calculated, this becomes a two step process:

- Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon

and underlying frequency and severity distribution.

- Step 2: Combine the multiple loss distributions after considering the dependence between the

different UoMs. The 'dependence' recognizes that the various UoMs are not completely

independent, ie the loss distributions are not additive, and that there is a sort of diversification

benefit in the sense that not all types of losses can occur at once and the joint probabilities of the

different losses make the sum less than the sum of the parts.

Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a

frequency distribution. Then n losses are picked from the severity distribution, and the total loss for

the year is a summation of these losses. This becomes one data point. This process of simulating the

number of losses and then identifying that number of losses is carried out a large number of times to

get the aggregate loss distribution for a UoM.

Step 2 requires taking the different loss distributions from Step 1 and combining them considering

the dependence between the events. The correlations between the losses are described by a

'copula', and combined together mathematically to get a single loss distribution for the entire bank.

This allows the 99.9th percentile loss to be calculated.