A potential decrease in capital reservation required by the regulator motivates banks to use advanced approaches to operational risk assessment. The acturial approach may also be useful from the standpoint of controlling the operational risks. The loss distribution approach, among others, is now considerably popular in banks all over the world. This paper shows why operational risk frequency and severity should be modeled separately under the LDA method and examines some problems regarding the modeling of operational loss severities. The study provides a complete scheme for using LDA. It gives arguments in support of using more complicated models against the simpler ones and vice versa as well. This paper analyses the connections between different distributions used to model operational risk. It emphasizes three distinctive features of operational risk data, i. e., skewness, kurtosis and a presence of the heavy tail. The notion of «fat tail» is re-introduced in comparison with the heavy tail. The article offers several graphical procedures to determine the presence of the heavy tail in a sample of operational risk data. Authors substantiate the need to use statistical models with two or more parameters. Theoretical aspects of EVT application to operational risk modeling are given. This study notes the POT method threshold choice dilemma and analyzes four different approaches to find the value of this threshold. The methods considered in this paper make up a powerful mathematical apparatus for operational risk modelling. However, some weak spots of the popular POT method are shown. Application of certain generalized models for operational risk modeling is suggested for further study.