# Estimating the Operational Risk (OpRisk) capital charge for a financial institute

This model estimates the total loss distribution from operational risks at a financial institute in order to estimate the capital charge necessary to cover the risk at a particular level of confidence.

Minimum software requirements: ModelRisk Complete edition. For complex OpRisk modeling, we recommend our specialist product StopRisk.

Technical difficulty: 3

Techniques used: Monte Carlo simulation in Excel, Lognormal distribution, Poisson distribution, Gaussian copula, FFT aggregate distribution construction

ModelRisk functions used: VoseLognormalObject, VosePoissonObject, VoseAggregateFFT, VoseValidCorrmat, VoseCopulaMultiNormal, VoseInput, VoseOutput

# Model description

The risk analysis model is built using Excel with our Monte Carlo simulation add-in called ModelRisk. It uses the following formatting convention:

The model comprises two sections. The first section is used to construct the copula use for correlating the aggregate losses from each Basel cell:

On the left table, correlation coefficients are entered. The top middle table then checks these coefficients and makes the smallest possible correction, if needed, to have a consistent correlation matrix, using the VoseValidCorrmat function. The colored table is there simply to illustrate the changes made by this function.

The single column table to the right uses the VoseCopulaMultiNormal function to simulate copula values using the corrected correlation matrix.

The second part of the model arranges data and functions by business line / event type combination:

From top to bottom, left to right:

A table of indices used to refer to that business line/ event type combination

• The mean size of a loss of this type M
• The standard deviation of losses of this type S
• The annual expected frequency of losses of this type L
• The copula value to use, selecting from the vector of copula values using the index from the first table
• The simulated aggregate loss for this type of loss. This uses the formula:
=VoseAggregateFFT(VosePoissonObject(L),VoseLognormalObject(M,S),,CopulaValue)
At the bottom, the aggregate losses are summed to give the model output.

# Results

The model takes about 90 seconds to run 50,000 samples. It is set up to directly show four reports within the ModelRisk ResultsViewer at the end of the simulation, which are described below.

The first tab shows a histogram plot of the total OpRisk loss distribution:

One can see, for example, that the most likely cost is around \$2.4 billion. The second tab shows the tornado sensitivity plot to individual cells for the P99 (the loss value one has 99% confidence of falling below):

One can see, for example, that the business line 3, event type 2 contributes the greatest uncertainty.

The third tab looks the P99 sensitivity to total losses by business line:

The fourth by event type:
And the last tab shows the cumulative descending plot for the total loss, from which we can read a P99 of \$3.350B: