Monte Carlo Simulations

Monte Carlo simulations are used extensively in market risk analysis, generally with historical rates data. As extensive data is available the simulation technique allows correlations between different data series to be taken into account.

In operational risk measurement Monte Carlo simulations are used differently. They are used to construct empirical risk distributions for segments based on the estimated individual risk distributions for each of the risks associated with that segment.

For operational risk the simulation involves running through thousands of iterations or hypothetical "years", with randomly generated inputs applied to the underlying risk distributions and the outcomes tabulated at the segment and Group level. The simulation is continued until the resulting empirical distribution at the targeted segment and Group levels become statistically stable enough to calculate their unexpected loss figures at the appropriate confidence level.

Note how the use of the Monte Carlo simulation places no constraints on the shapes of the underlying individual risk distributions, except that they provide a numerical response to a randomly generated input. It is possible to use individual risk distributions that are continuous or discrete, and to use distributions that recognise an upside gain as well as those that recognise only loss potential.

The main problem with the approach is with the assumption to this point that each of the underlying individual risks are independent of each other. That is, that the randomly generated result of one risk has no influence, positive or negative, on the results of other risks. Clearly this is not realistic. A control culture in an organisation affects many risks, as does a change in economic conditions or legal interpretation. This leads us to consider correlations between risks.

To Correlations between risks

Last updated:16/5/07

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