Financial risks are considered today as popular research topics due to the existing practical necessity for the use of their mathematical models, estimates of possible loss in many areas of human activities, forecasting, and respective managerial decisions in financial and other spheres where capital, obligations, stocks, bonds, and other activities are circulating successfully. Financial processes today exhibit sophisticated forms of evolution in time that require the application of sophisticated modeling, risk estimating, forecasting, and decision-making/support methods, techniques, and procedures. The system analysis approach is applied to solving such problems as a unique and universal research methodology. The financial risks, specifically the operational ones in the study considered, are classified as nonlinear and nonstationary processes that require appropriate methods for analysis and a rather sophisticated analytical description to estimate and forecast possible loss. The results of operational risk analysis are achieved in the form of systemic methodology, models constructed with statistical data, regression analysis, and Bayesian techniques, and estimated loss with the models. The models and system analysis approach proposed for analyzing financial processes are suitable for practical applications, provided the users have appropriate statistical data and expert estimates.