Abstract: According to the extreme value statistical theory, unexpected loss estimation in a heavy-tailed distribution objectively has uncertainty that cannot be neglected in a high confidence level. Existing empirical research shows that the operating loss intensity distribution has a significant heavy-tailed quality. Therefore, under the loss distribution approach, namely in the composite distribution compounded of heavy-tailed operating loss intensity distribution and loss frequency distribution, the regulatory capital of operational risk is in great uncertainty that cannot be neglected. The uncertainty of regulatory capital is mainly from model error and measurement error. In the existing theory, the model biases are unpredictable, and only the model parameter estimation error caused by the measurement error can be predicted. Therefore, in the condition of fixing measurement model and the model deviation is invariable, only the measurement error changes.
Theoretical research shows that only Pareto distribution is heavy-tailed distribution in the generalized Pareto distribution. Therefore, the operational risk measurement is taken for example in this paper. After measuring error variation by loss distribution approach in Pareto distribution, it is found:As the operational risk increases and the regulatory capital increases progressively, and under the influence of characteristics parameters of loss intensity distribution, the measurement error increases. Under the influence of frequency parameters, when the shape parameter is greater than 1, the measurement error increases. However, when the shape parameter is less than 1, the measurement error trend line has multiple extreme points. Furthermore, according to the fitting results of operating loss frequency distribution and loss intensity distribution using the Basel committee operating loss data samples, they can verify the validity of the proposed theoretical model in this paper.
Thus' it can be seen that with the changes in regulatory capital, the measurement error changes in high sensitivity, and this means that the measurement error of regulatory capital is unpredictable. Within the range of measurement error, there exists the extreme points, and in the condition of these extreme risk, the measurement error becomes very large (tends to infinity) in relative to the regulatory capital. At this moment, the reliability of the measurement results cannot be accurately evaluated. Obviously, when loss intensity distribution is a heavy-tail distribution, the measurement results may appear serious faults with the loss distribution approach in a high confidence level. Furthermore, the regularity of error variation measured by loss distribution approach when the loss intensity has a significant heavy tail and lays a theoretical foundation for applying LDA in heavy-tailed risk measurement is explored.

Key words: operational risk, loss distribution approach, error propagation theory, measurement error